// Numbas version: exam_results_page_options
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3pt;\"></p>\n<p style=\"float: right; padding: 3pt;\"></p>\n<p>A chemical plant consists for&nbsp;3 loads</p>\n<ul>\n<li>Load 1 : {P1} kW at a power factor of {pf1} lagging</li>\n<li>Load 2 : {S2} kVA at a power factor of {pf2} lagging</li>\n<li>Load 3 : {abs(Q3)} kVAr capacitor bank</li>\n</ul>\n<p>(a) Calculate the total power factor of the power consumed by these loads in the chemical plant.</p>\n<p>(b) Determine the size of capacitor required (in kVAr) to ensure unity power factor.</p>\n<p>(c) Determine the size of capacitor required (in kVAr) to achive a power factor of at least 0.95.&nbsp;</p>\n<p></p>", "advice": "", "rulesets": {}, "extensions": ["geogebra", "quantities", "weh"], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"P1": {"name": "P1", "group": "Given in question", "definition": "random(10 .. 20#1)", "description": "<p>kW</p>", "templateType": "randrange", "can_override": false}, "pf1": {"name": "pf1", "group": "Given in question", "definition": "random(0.6 .. 0.75#0.05)", "description": "", "templateType": "randrange", "can_override": false}, "S1": {"name": "S1", "group": "Calculated values", "definition": "P1/pf1", "description": "", "templateType": "anything", "can_override": false}, "S2": {"name": "S2", "group": "Given in question", "definition": "random(8 .. 15#1)", "description": "", "templateType": "randrange", "can_override": false}, "Q1": {"name": "Q1", "group": "Calculated values", "definition": "sqrt(S1^2-P1^2)", "description": "", "templateType": "anything", "can_override": false}, "P2": {"name": "P2", "group": "Calculated values", "definition": "S2*pf2", "description": "", "templateType": "anything", "can_override": false}, "Q2": {"name": "Q2", "group": "Calculated values", "definition": "sqrt(S2^2-P2^2)", "description": "", "templateType": "anything", "can_override": false}, "pf2": {"name": "pf2", "group": "Given in question", "definition": "random(0.6 .. 0.9#0.1)", "description": "", 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"variables": ["minTol", "maxTol"]}], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": true, "customName": "Examine each load", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Complete the follwoing table&nbsp;</p>\n<table border=\"1\">\n<tbody>\n<tr>\n<td></td>\n<td><strong>P&nbsp;</strong></td>\n<td><strong>Q</strong></td>\n<td><strong>S</strong></td>\n</tr>\n<tr>\n<td><strong>Load 1</strong></td>\n<td>[[0]]&nbsp;kW</td>\n<td>[[3]] kVAr</td>\n<td>[[6]]&nbsp;kVA</td>\n</tr>\n<tr>\n<td><strong>Load 2</strong></td>\n<td>[[1]] kW</td>\n<td>[[4]]&nbsp;kVAr</td>\n<td>[[7]]&nbsp;kVA</td>\n</tr>\n<tr>\n<td><strong>Load 3</strong></td>\n<td>[[2]] kW</td>\n<td>[[5]] kVAr</td>\n<td>\n<p>[[8]]&nbsp;kVA</p>\n</td>\n</tr>\n</tbody>\n</table>\n<p></p>", "stepsPenalty": "4.5", "steps": [{"type": "information", "useCustomName": true, "customName": "Help", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<div class=\"content-area\">\n<p>Use units to help know what info you are given;</p>\n<ul>\n<li>kW measures Real or Active Power, P</li>\n<li>kW measures Imag or Reactive Power, Q&nbsp; &nbsp;... be very carefule here on sign of Q.</li>\n<li>kW measures Total or Apparant Power, S</li>\n</ul>\n<p>If you know any two from these five variables, <span style=\"font-size: 15px; white-space: nowrap;\">P, Q, S , pf and $\\theta$ ...</span></p>\n<p><span style=\"font-size: 15px; white-space: nowrap;\">...&nbsp; then you can always find the other values using these two equations</span><span style=\"font-size: 15px; white-space: nowrap;\"></span></p>\n<ul>\n<li><span style=\"font-size: 15px; white-space: nowrap;\">$P^2+Q^2 = |S|^2$</span></li>\n<li><span style=\"font-size: 15px; white-space: nowrap;\">$pf = cos(\\theta) = \\frac{P}{|S|}$</span></li>\n</ul>\n<p></p>\n<p>Also, you will need to be careful with polarity of reactive power depeding on leading or lagging loads.&nbsp;&nbsp;</p>\n<p>Inductors will have +Q values. Capactitors are the opposite. (i.e. -Q values)</p>\n<p>CIVIL ...use this to work if Cap or Inductor.&nbsp;&nbsp;</p>\n<p>e.g.&nbsp; current __________ voltage (lead or lag)</p>\n<p></p>\n</div>"}], "gaps": [{"type": "numberentry", "useCustomName": true, "customName": "P1", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "P1*minTol", "maxValue": "P1*maxTol", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": true, "customName": "P2", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", 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"scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "Q2*minTol", "maxValue": "Q2*maxTol", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": true, "customName": "Q3", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "Q3*minTol", "maxValue": "Q3*maxTol", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": true, "customName": "S1", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "abs(S1)*minTol", "maxValue": "abs(S1)*maxTol", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": true, "customName": "S2", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "abs(S2)*minTol", "maxValue": "abs(S2)*maxTol", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": true, "customName": "S3", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "abs(S3)*minTol", "maxValue": "abs(S3)*maxTol", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": true, "customName": "(a) Total Load", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>The combined load is there for&nbsp;$($[[0]]}$\\angle $[[1]]$^{\\circ}) kVA = $&nbsp;[[2]]&nbsp;$kW + j$[[3]] $kVAr$</p>\n<p>And the uncorrected power factor is&nbsp;[[4]].</p>\n<p></p>", "stepsPenalty": "2.5", "steps": [{"type": "information", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Add all the real power values to get $P_{total}$</p>\n<p>Add all the reactive power values to get $Q_{total}$</p>\n<p>Then find total apparent power&nbsp;$S_{total} = P_{total} +jQ_{total}$&nbsp;</p>\n<p>Finaly, convert from rectangular to polar form.&nbsp;</p>"}], "gaps": [{"type": "numberentry", "useCustomName": true, "customName": "Smag", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "abs(Stotal)*minTol", "maxValue": "abs(Stotal)*maxTol", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": true, "customName": "Sph", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "arg(Stotal)*(180/pi) *minTol", "maxValue": "arg(Stotal)*(180/pi)*maxTol", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": true, "customName": "P", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "Ptotal*minTol", "maxValue": "Ptotal*maxTol", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": true, "customName": "Q", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "Qtotal*minTol", "maxValue": "Qtotal*maxTol", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": true, "customName": "pfTotal", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "pfUncorrected*minTol", "maxValue": "pfUncorrected*maxTol", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": true, "customName": "(b) PFCunity", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>An additional capacative load of&nbsp;[[0]] kVar is required to correct the overall power factor to unity.</p>", "stepsPenalty": "0.5", "steps": [{"type": "information", "useCustomName": true, "customName": "Help with finding Qpfc", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>In these questions, we know two things about how the newTotal load will look</p>\n<ul>\n<li>New Total Load will have&nbsp; pf=1</li>\n<li>New Total Load will have the same real power, P, as before. P = {round(Ptotal)} kW</li>\n</ul>\n<table style=\"height: 90px; width: 365px; border-style: solid; border-color: #000000;\">\n<tbody>\n<tr style=\"height: 18px;\">\n<td style=\"width: 74.75px; height: 18px; border-style: solid; border-color: #000000;\"></td>\n<td style=\"width: 111.625px; height: 18px; border-style: solid; border-color: #000000;\">\n<p>P</p>\n<p>[kW]</p>\n</td>\n<td style=\"width: 114.203px; height: 18px; border-style: solid; border-color: #000000;\">\n<p>Q</p>\n<p>[kVAr]</p>\n</td>\n<td style=\"width: 9.84375px; border-style: solid; border-color: #000000;\">S [kVA]</td>\n<td style=\"width: 13.6562px; height: 18px; border-style: solid; border-color: #000000;\">pf</td>\n<td style=\"width: 73.5156px; border-style: solid; border-color: #000000;\">$|\\theta|$</td>\n</tr>\n<tr style=\"height: 18px;\">\n<td style=\"width: 74.75px; height: 18px; border-style: solid; border-color: #000000;\">Original Load</td>\n<td style=\"width: 111.625px; height: 18px; border-style: solid; border-color: #000000;\">{round(Ptotal)}</td>\n<td style=\"width: 114.203px; height: 18px; border-style: solid; border-color: #000000;\">{round(Qtotal)}</td>\n<td style=\"width: 9.84375px; border-style: solid; border-color: #000000;\">&nbsp; &nbsp; &nbsp; &nbsp;&nbsp;</td>\n<td style=\"width: 13.6562px; height: 18px; border-style: solid; border-color: #000000;\"></td>\n<td style=\"width: 73.5156px; border-style: solid; border-color: #000000;\"></td>\n</tr>\n<tr style=\"height: 18px;\">\n<td style=\"width: 74.75px; height: 18px; border-style: solid; border-color: #000000;\">Additional&nbsp; PFC&nbsp;</td>\n<td style=\"width: 111.625px; height: 18px; border-style: solid; border-color: #000000;\">0</td>\n<td style=\"width: 114.203px; height: 18px; border-style: solid; border-color: #000000;\"></td>\n<td style=\"width: 9.84375px; border-style: solid; border-color: #000000;\"></td>\n<td style=\"width: 13.6562px; height: 18px; border-style: solid; border-color: #000000;\"></td>\n<td style=\"width: 73.5156px; border-style: solid; border-color: #000000;\"></td>\n</tr>\n<tr style=\"height: 36px;\">\n<td style=\"width: 74.75px; height: 36px; border-style: solid; border-color: #000000;\">New Total Load = OrigLoad + PFC</td>\n<td style=\"width: 111.625px; height: 36px; border-style: solid; border-color: #000000;\">{round(Ptotal)}</td>\n<td style=\"width: 114.203px; height: 36px; border-style: solid; border-color: #000000;\"></td>\n<td style=\"width: 9.84375px; border-style: solid; border-color: #000000;\">{round(Ptotal)}</td>\n<td style=\"width: 13.6562px; height: 36px; border-style: solid; border-color: #000000;\">1</td>\n<td style=\"width: 73.5156px; border-style: solid; border-color: #000000;\"></td>\n</tr>\n</tbody>\n</table>\n<p>Now working on the New Total Row, we know 2 of the 5 variables.&nbsp; So we can calulate the others</p>\n<p>(we are really only intersted in Q so we'll only work that one out.)</p>\n<p>Since $pf=\\frac{P}{|S|} $, we have |S|= {round(Ptotal)}&nbsp; therefore Q = 0&nbsp;</p>\n<table style=\"height: 90px; width: 365px; border-style: solid; border-color: #000000;\">\n<tbody>\n<tr style=\"height: 18px;\">\n<td style=\"width: 74.75px; height: 18px; border-style: solid; border-color: #000000;\"></td>\n<td style=\"width: 111.625px; height: 18px; border-style: solid; border-color: #000000;\">P [kW]</td>\n<td style=\"width: 114.203px; height: 18px; border-style: solid; border-color: #000000;\">Q [kVAr]</td>\n<td style=\"width: 9.57812px; border-style: solid; border-color: #000000;\">&nbsp;S [kVA]</td>\n<td style=\"width: 13.6562px; height: 18px; border-style: solid; border-color: #000000;\">pf</td>\n<td style=\"width: 73.5156px; border-style: solid; border-color: #000000;\">$|\\theta|$</td>\n</tr>\n<tr style=\"height: 18px;\">\n<td style=\"width: 74.75px; height: 18px; border-style: solid; border-color: #000000;\">Original Load</td>\n<td style=\"width: 111.625px; height: 18px; border-style: solid; border-color: #000000;\">{round(Ptotal)}</td>\n<td style=\"width: 114.203px; height: 18px; border-style: solid; border-color: #000000;\">{round(Qtotal)}</td>\n<td style=\"width: 9.57812px; border-style: solid; border-color: #000000;\"></td>\n<td style=\"width: 13.6562px; height: 18px; border-style: solid; border-color: #000000;\"></td>\n<td style=\"width: 73.5156px; border-style: solid; border-color: #000000;\"></td>\n</tr>\n<tr style=\"height: 18px;\">\n<td style=\"width: 74.75px; height: 18px; border-style: solid; border-color: #000000;\">Additional&nbsp; PFC&nbsp;</td>\n<td style=\"width: 111.625px; height: 18px; border-style: solid; border-color: #000000;\">0</td>\n<td style=\"width: 114.203px; height: 18px; border-style: solid; border-color: #000000;\"></td>\n<td style=\"width: 9.57812px; border-style: solid; border-color: #000000;\"></td>\n<td style=\"width: 13.6562px; height: 18px; border-style: solid; border-color: #000000;\"></td>\n<td style=\"width: 73.5156px; border-style: solid; border-color: #000000;\"></td>\n</tr>\n<tr style=\"height: 36px;\">\n<td style=\"width: 74.75px; height: 36px; border-style: solid; border-color: #000000;\">New Total Load = OrigLoad + PFC</td>\n<td style=\"width: 111.625px; height: 36px; border-style: solid; border-color: #000000;\">{round(Ptotal)}</td>\n<td style=\"width: 114.203px; height: 36px; border-style: solid; border-color: #000000;\"><strong>0</strong></td>\n<td style=\"width: 9.57812px; border-style: solid; border-color: #000000;\">{round(Ptotal)}</td>\n<td style=\"width: 13.6562px; height: 36px; border-style: solid; border-color: #000000;\">1</td>\n<td style=\"width: 73.5156px; border-style: solid; border-color: #000000;\"></td>\n</tr>\n</tbody>\n</table>\n<p>Final step, looking down the Q column ...&nbsp;</p>\n<p>NewTotal Q = Orig Load Q + Qpfc&nbsp;</p>\n<p>0 = {round(Qtotal)} + Qpfc</p>\n<p>Qpfc = {round(Qtotal*-1)}</p>\n<p></p>\n<table style=\"height: 90px; width: 365px; border-style: solid; border-color: #000000;\">\n<tbody>\n<tr style=\"height: 18px;\">\n<td style=\"width: 74.75px; height: 18px; border-style: solid; border-color: #000000;\"></td>\n<td style=\"width: 111.625px; height: 18px; border-style: solid; border-color: #000000;\">P [kW]</td>\n<td style=\"width: 138.359px; height: 18px; border-style: solid; border-color: #000000;\">Q [kVAr]</td>\n<td style=\"width: 39.7344px; border-style: solid; border-color: #000000;\">S [kVA]</td>\n<td style=\"width: 13.6562px; height: 18px; border-style: solid; border-color: #000000;\">pf</td>\n<td style=\"width: 73.5156px; border-style: solid; border-color: #000000;\">$|\\theta|$</td>\n</tr>\n<tr style=\"height: 18px;\">\n<td style=\"width: 74.75px; height: 18px; border-style: solid; border-color: #000000;\">Original Load</td>\n<td style=\"width: 111.625px; height: 18px; border-style: solid; border-color: #000000;\">{round(Ptotal)}</td>\n<td style=\"width: 138.359px; height: 18px; border-style: solid; border-color: #000000;\">{round(Qtotal)}</td>\n<td style=\"width: 39.7344px; border-style: solid; border-color: #000000;\"></td>\n<td style=\"width: 13.6562px; height: 18px; border-style: solid; border-color: #000000;\"></td>\n<td style=\"width: 73.5156px; border-style: solid; border-color: #000000;\"></td>\n</tr>\n<tr style=\"height: 18px;\">\n<td style=\"width: 74.75px; height: 18px; border-style: solid; border-color: #000000;\">Additional&nbsp; PFC&nbsp;</td>\n<td style=\"width: 111.625px; height: 18px; border-style: solid; border-color: #000000;\">0</td>\n<td style=\"width: 138.359px; height: 18px; border-style: solid; border-color: #000000;\">{round(Qtotal*-1)}</td>\n<td style=\"width: 39.7344px; border-style: solid; border-color: #000000;\"></td>\n<td style=\"width: 13.6562px; height: 18px; border-style: solid; border-color: #000000;\"></td>\n<td style=\"width: 73.5156px; border-style: solid; border-color: #000000;\"></td>\n</tr>\n<tr style=\"height: 36px;\">\n<td style=\"width: 74.75px; height: 36px; border-style: solid; border-color: #000000;\">New Total Load = OrigLoad + PFC</td>\n<td style=\"width: 111.625px; height: 36px; border-style: solid; border-color: #000000;\">{round(Ptotal)}</td>\n<td style=\"width: 138.359px; height: 36px; border-style: solid; border-color: #000000;\">0</td>\n<td style=\"width: 39.7344px; border-style: solid; border-color: #000000;\">{round(Ptotal)}</td>\n<td style=\"width: 13.6562px; height: 36px; border-style: solid; border-color: #000000;\">1</td>\n<td style=\"width: 73.5156px; border-style: solid; border-color: #000000;\"></td>\n</tr>\n</tbody>\n</table>"}], "gaps": [{"type": "numberentry", "useCustomName": true, "customName": "QTotal needed", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "abs(Qtotal)*minTol", "maxValue": "abs(Qtotal)*maxTol", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": true, "customName": "(c) PFC", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>An additional capacative load of&nbsp;[[0]] kVar is required to correct the overall power factor to 0.95.</p>", "stepsPenalty": "0.5", "steps": [{"type": "information", "useCustomName": true, "customName": "Help with finding Qpfc", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p><em>WARNING </em></p>\n<p><em>I've round the values in this solution to make it readable ... you will need to keep a few decimal places. </em></p>\n<p><em>JR Nov'21</em></p>\n<p></p>\n<p>In these questions, we know two things about how the newTotal load will look</p>\n<ul>\n<li>New Total Load will have&nbsp; pf=0.95</li>\n<li>New Total Load will have the same real power, P, as before. P = {round(Ptotal)} kW</li>\n</ul>\n<table style=\"height: 90px; width: 365px; border-style: solid; border-color: #000000;\">\n<tbody>\n<tr style=\"height: 18px;\">\n<td style=\"width: 74.75px; height: 18px; border-style: solid; border-color: #000000;\"></td>\n<td style=\"width: 111.625px; height: 18px; border-style: solid; border-color: #000000;\">\n<p>P</p>\n<p>[kW]</p>\n</td>\n<td style=\"width: 114.203px; height: 18px; border-style: solid; border-color: #000000;\">\n<p>Q</p>\n<p>[kVAr]</p>\n</td>\n<td style=\"width: 9.84375px; border-style: solid; border-color: #000000;\">S [kVA]</td>\n<td style=\"width: 13.6562px; height: 18px; border-style: solid; border-color: #000000;\">pf</td>\n<td style=\"width: 73.5156px; border-style: solid; border-color: #000000;\">$|\\theta|$</td>\n</tr>\n<tr style=\"height: 18px;\">\n<td style=\"width: 74.75px; height: 18px; border-style: solid; border-color: #000000;\">Original Load</td>\n<td style=\"width: 111.625px; height: 18px; border-style: solid; border-color: #000000;\">{round(Ptotal)}</td>\n<td style=\"width: 114.203px; height: 18px; border-style: solid; border-color: #000000;\">{round(Qtotal)}</td>\n<td style=\"width: 9.84375px; border-style: solid; border-color: #000000;\">&nbsp; &nbsp; &nbsp; &nbsp;&nbsp;</td>\n<td style=\"width: 13.6562px; height: 18px; border-style: solid; border-color: #000000;\"></td>\n<td style=\"width: 73.5156px; border-style: solid; border-color: #000000;\"></td>\n</tr>\n<tr style=\"height: 18px;\">\n<td style=\"width: 74.75px; height: 18px; border-style: solid; border-color: #000000;\">Additional&nbsp; PFC&nbsp;</td>\n<td style=\"width: 111.625px; height: 18px; border-style: solid; border-color: #000000;\">0</td>\n<td style=\"width: 114.203px; height: 18px; border-style: solid; border-color: #000000;\"></td>\n<td style=\"width: 9.84375px; border-style: solid; border-color: #000000;\"></td>\n<td style=\"width: 13.6562px; height: 18px; border-style: solid; border-color: #000000;\"></td>\n<td style=\"width: 73.5156px; border-style: solid; border-color: #000000;\"></td>\n</tr>\n<tr style=\"height: 36px;\">\n<td style=\"width: 74.75px; height: 36px; border-style: solid; border-color: #000000;\">New Total Load = OrigLoad + PFC</td>\n<td style=\"width: 111.625px; height: 36px; border-style: solid; border-color: #000000;\">{round(Ptotal)}</td>\n<td style=\"width: 114.203px; height: 36px; border-style: solid; border-color: #000000;\">???</td>\n<td style=\"width: 9.84375px; border-style: solid; border-color: #000000;\">???</td>\n<td style=\"width: 13.6562px; height: 36px; border-style: solid; border-color: #000000;\">0.95</td>\n<td style=\"width: 73.5156px; border-style: solid; border-color: #000000;\"></td>\n</tr>\n</tbody>\n</table>\n<p>Now working on the New Total Row, we know 2 of the 5 variables.&nbsp; So we can calulate the others</p>\n<p>(we are really only intersted in Q so we'll only work that one out.)</p>\n<p>Since $pf=\\frac{P}{|S|} $, we have |S|= {round(Ptotal)} * 0.95&nbsp; therefore Q = {round(QtotalRequired)}</p>\n<table style=\"height: 90px; width: 365px; border-style: solid; border-color: #000000;\">\n<tbody>\n<tr style=\"height: 18px;\">\n<td style=\"width: 74.75px; height: 18px; border-style: solid; border-color: #000000;\"></td>\n<td style=\"width: 111.625px; height: 18px; border-style: solid; border-color: #000000;\">P [kW]</td>\n<td style=\"width: 114.203px; height: 18px; border-style: solid; border-color: #000000;\">Q [kVAr]</td>\n<td style=\"width: 9.57812px; border-style: solid; border-color: #000000;\">&nbsp;S [kVA]</td>\n<td style=\"width: 13.6562px; height: 18px; border-style: solid; border-color: #000000;\">pf</td>\n<td style=\"width: 73.5156px; border-style: solid; border-color: #000000;\">$|\\theta|$</td>\n</tr>\n<tr style=\"height: 18px;\">\n<td style=\"width: 74.75px; height: 18px; border-style: solid; border-color: #000000;\">Original Load</td>\n<td style=\"width: 111.625px; height: 18px; border-style: solid; border-color: #000000;\">{round(Ptotal)}</td>\n<td style=\"width: 114.203px; height: 18px; border-style: solid; border-color: #000000;\">{round(Qtotal)}</td>\n<td style=\"width: 9.57812px; border-style: solid; border-color: #000000;\"></td>\n<td style=\"width: 13.6562px; height: 18px; border-style: solid; border-color: #000000;\"></td>\n<td style=\"width: 73.5156px; border-style: solid; border-color: #000000;\"></td>\n</tr>\n<tr style=\"height: 18px;\">\n<td style=\"width: 74.75px; height: 18px; border-style: solid; border-color: #000000;\">Additional&nbsp; PFC&nbsp;</td>\n<td style=\"width: 111.625px; height: 18px; border-style: solid; border-color: #000000;\">0</td>\n<td style=\"width: 114.203px; height: 18px; border-style: solid; border-color: #000000;\">????</td>\n<td style=\"width: 9.57812px; border-style: solid; border-color: #000000;\"></td>\n<td style=\"width: 13.6562px; height: 18px; border-style: solid; border-color: #000000;\"></td>\n<td style=\"width: 73.5156px; border-style: solid; border-color: #000000;\"></td>\n</tr>\n<tr style=\"height: 36px;\">\n<td style=\"width: 74.75px; height: 36px; border-style: solid; border-color: #000000;\">New Total Load = OrigLoad + PFC</td>\n<td style=\"width: 111.625px; height: 36px; border-style: solid; border-color: #000000;\">{round(Ptotal)}</td>\n<td style=\"width: 114.203px; height: 36px; border-style: solid; border-color: #000000;\"><strong>{round(QtotalRequired)}</strong></td>\n<td style=\"width: 9.57812px; border-style: solid; border-color: #000000;\"><strong>{round(SrequiredMag)}</strong></td>\n<td style=\"width: 13.6562px; height: 36px; border-style: solid; border-color: #000000;\">0.95</td>\n<td style=\"width: 73.5156px; border-style: solid; border-color: #000000;\"></td>\n</tr>\n</tbody>\n</table>\n<p>Final step, looking down the Q column ...&nbsp;</p>\n<p>NewTotal Q = Orig Load Q + Qpfc&nbsp;</p>\n<p>{round(QtotalRequired)} = {round(Qtotal)} + Qpfc</p>\n<p>Qpfc = {round(QtotalRequired)} - {round(Qtotal)}&nbsp;</p>\n<p></p>\n<table style=\"height: 90px; width: 365px; border-style: solid; border-color: #000000;\">\n<tbody>\n<tr style=\"height: 18px;\">\n<td style=\"width: 74.75px; height: 18px; border-style: solid; border-color: #000000;\"></td>\n<td style=\"width: 111.625px; height: 18px; border-style: solid; border-color: #000000;\">P [kW]</td>\n<td style=\"width: 138.359px; height: 18px; border-style: solid; border-color: #000000;\">Q [kVAr]</td>\n<td style=\"width: 39.7344px; border-style: solid; border-color: #000000;\">S [kVA]</td>\n<td style=\"width: 13.6562px; height: 18px; border-style: solid; border-color: #000000;\">pf</td>\n<td style=\"width: 73.5156px; border-style: solid; border-color: #000000;\">$|\\theta|$</td>\n</tr>\n<tr style=\"height: 18px;\">\n<td style=\"width: 74.75px; height: 18px; border-style: solid; border-color: #000000;\">Original Load</td>\n<td style=\"width: 111.625px; height: 18px; border-style: solid; border-color: #000000;\">{round(Ptotal)}</td>\n<td style=\"width: 138.359px; height: 18px; border-style: solid; border-color: #000000;\">{round(Qtotal)}</td>\n<td style=\"width: 39.7344px; border-style: solid; border-color: #000000;\"></td>\n<td style=\"width: 13.6562px; height: 18px; border-style: solid; border-color: #000000;\"></td>\n<td style=\"width: 73.5156px; border-style: solid; border-color: #000000;\"></td>\n</tr>\n<tr style=\"height: 18px;\">\n<td style=\"width: 74.75px; height: 18px; border-style: solid; border-color: #000000;\">Additional&nbsp; PFC&nbsp;</td>\n<td style=\"width: 111.625px; height: 18px; border-style: solid; border-color: #000000;\">0</td>\n<td style=\"width: 138.359px; height: 18px; border-style: solid; border-color: #000000;\"><strong>{round(QtotalRequired)} - {round(Qtotal)} ={round(Qpfc)}</strong></td>\n<td style=\"width: 39.7344px; border-style: solid; border-color: #000000;\"></td>\n<td style=\"width: 13.6562px; height: 18px; border-style: solid; border-color: #000000;\"></td>\n<td style=\"width: 73.5156px; border-style: solid; border-color: #000000;\"></td>\n</tr>\n<tr style=\"height: 36px;\">\n<td style=\"width: 74.75px; height: 36px; border-style: solid; border-color: #000000;\">New Total Load = OrigLoad + PFC</td>\n<td style=\"width: 111.625px; height: 36px; border-style: solid; border-color: #000000;\">{round(Ptotal)}</td>\n<td style=\"width: 138.359px; height: 36px; border-style: solid; border-color: #000000;\">{round(QtotalRequired)}</td>\n<td style=\"width: 39.7344px; border-style: solid; border-color: #000000;\">{round(SrequiredMag)}</td>\n<td style=\"width: 13.6562px; height: 36px; border-style: solid; border-color: #000000;\">1</td>\n<td style=\"width: 73.5156px; border-style: solid; border-color: #000000;\"></td>\n</tr>\n</tbody>\n</table>\n<p></p>"}], "gaps": [{"type": "numberentry", "useCustomName": true, "customName": "Qpfc needed", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "abs(Qpfc)*minTol", "maxValue": "abs(Qpfc)*maxTol", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "contributors": [{"name": "William Haynes", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2530/"}, {"name": "Judy Rea", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/8753/"}]}]}], "contributors": [{"name": "William Haynes", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2530/"}, {"name": "Judy Rea", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/8753/"}]}