// Numbas version: finer_feedback_settings
{"name": "ElQ3 - Power & Frequency Response  - Randomised Variables Only", "extensions": [], "custom_part_types": [], "resources": [["question-resources/SbE_CC1_Q3ai.png", "/srv/numbas/media/question-resources/SbE_CC1_Q3ai.png"], ["question-resources/SbE_CC1_Q3b.png", "/srv/numbas/media/question-resources/SbE_CC1_Q3b.png"], ["question-resources/SbE_CC1_Q3d.png", "/srv/numbas/media/question-resources/SbE_CC1_Q3d.png"], ["question-resources/SbE_CC1_Q3c.png", "/srv/numbas/media/question-resources/SbE_CC1_Q3c.png"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "ElQ3 - Power & Frequency Response  - Randomised Variables Only", "tags": [], "metadata": {"description": "<p>Question Covering AC power and frquency response</p>", "licence": "All rights reserved"}, "statement": "<h2 style=\"text-align: center;\">Power &amp; Frequency Response</h2>", "advice": "<p>see spread sheet</p>", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"Q3ai_f_S": {"name": "Q3ai_f_S", "group": "Q3a", "definition": "random(100 .. 150#10)", "description": "<p>Frequency (f<sub>s</sub>)</p>", "templateType": "randrange", "can_override": false}, "Q3ai_V_PP": {"name": "Q3ai_V_PP", "group": "Q3a", "definition": "random(5 .. 9#1)", "description": "<p>V<sub>P-P</sub></p>", "templateType": "randrange", "can_override": false}, "Q3ai_V_DC": {"name": "Q3ai_V_DC", "group": "Q3a", "definition": "random(-0.5 .. 0.5#0.2)", "description": "<p style=\"text-align: left;\">DC Offset</p>", "templateType": "randrange", "can_override": false}, "Q3ai_R_L": {"name": "Q3ai_R_L", "group": "Q3a", "definition": "random(50 .. 150#10)", "description": "<p>Load Resistor R<sub>L</sub></p>", "templateType": "randrange", "can_override": false}, "q3aii_f_s": {"name": "q3aii_f_s", "group": "Q3a", "definition": "random(33 .. 99#33)", "description": "<p>Frequency (f<sub>s</sub>)</p>", "templateType": "randrange", "can_override": false}, "q3aii_v_pp": {"name": "q3aii_v_pp", "group": "Q3a", "definition": "random(5 .. 5#1)", "description": "<p>V<sub>P-P</sub></p>", "templateType": "randrange", "can_override": false}, "Q3aii_R_L": {"name": "Q3aii_R_L", "group": "Q3a", "definition": "random(2000 .. 2000#1)", "description": "<p>R<sub>L</sub></p>", "templateType": "randrange", "can_override": false}, "Q3aii_t_rise": {"name": "Q3aii_t_rise", "group": "Q3a", "definition": "siground(dec(1/(Q3aii_t_rise_modifier*q3aii_f_s)),4)", "description": "", "templateType": "anything", "can_override": false}, "Q3aii_t_rise_modifier": {"name": "Q3aii_t_rise_modifier", "group": "Q3a", "definition": "random(3 .. 4#1)", "description": "<p>Modifier of t_rise</p>", "templateType": "randrange", "can_override": false}, "Q3aii_V_DC": {"name": "Q3aii_V_DC", "group": "Q3a", "definition": "random(1 .. 1#1)", "description": "<p>DC Offset</p>", "templateType": "randrange", "can_override": false}, "Q3b_R1": {"name": "Q3b_R1", "group": "Q3b", "definition": "random(3000 .. 3600#100)", "description": "", "templateType": "randrange", "can_override": false}, "Q3b_R2": {"name": "Q3b_R2", "group": "Q3b", "definition": "random(2000 .. 2000#1000)", "description": "", "templateType": "randrange", "can_override": false}, "Q3b_R3": {"name": "Q3b_R3", "group": "Q3b", "definition": "random(1800 .. 2000#500)", "description": "", "templateType": "randrange", "can_override": false}, "Q3b_R4": {"name": "Q3b_R4", "group": "Q3b", "definition": "random(10000 .. 20000#2000)", "description": "", "templateType": "randrange", "can_override": false}, "Q3b_VS": {"name": "Q3b_VS", "group": "Q3b", "definition": "random(12 .. 12#1)", "description": "", "templateType": "randrange", "can_override": false}, "Q3c_R_L": {"name": "Q3c_R_L", "group": "Q3d", "definition": "random(1 .. 3#1)", "description": "<p>Load Resistance (k&Omega;)</p>", "templateType": "randrange", "can_override": false}, "Q3c_C1": {"name": "Q3c_C1", "group": "Q3d", "definition": "random(1 .. 3#1)", "description": "<p>Smoothing Capacitor (uF)</p>", "templateType": "randrange", "can_override": false}, "Q3c_V_S": {"name": "Q3c_V_S", "group": "Q3d", "definition": "random(20 .. 23#1)", "description": "<p>Supply Voltage (V<sub>S</sub>)</p>", "templateType": "randrange", "can_override": true}, "Q3c_Z_BDV": {"name": "Q3c_Z_BDV", "group": "Q3d", "definition": "siground(dec(q3c_v_s*(3/20)),2)", "description": "<p>Zener Diode Reverse Breakdown Voltage (V)</p>", "templateType": "anything", "can_override": false}, "Q3d_C1": {"name": "Q3d_C1", "group": "Q4d", "definition": "random(10 .. 12#0.1)", "description": "<p>Capacitance C1</p>", "templateType": "randrange", "can_override": false}, "Q3d_L1": {"name": "Q3d_L1", "group": "Q4d", "definition": "random(170 .. 190#10)", "description": "<p>Inductance</p>", "templateType": "randrange", "can_override": false}, "Q3d_R_L": {"name": "Q3d_R_L", "group": "Q4d", "definition": "random(1 .. 5#4)", "description": "", "templateType": "randrange", "can_override": false}, "Q3d_V_S": {"name": "Q3d_V_S", "group": "Q4d", "definition": "random(1 .. 10#9)", "description": "", "templateType": "randrange", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": [], "variable_groups": [{"name": "Unnamed group", "variables": []}, {"name": "Q3b", "variables": ["Q3b_R1", "Q3b_R2", "Q3b_R3", "Q3b_R4", "Q3b_VS"]}, {"name": "Q3a", "variables": ["Q3ai_f_S", "Q3ai_R_L", "Q3ai_V_DC", "Q3ai_V_PP", "q3aii_f_s", "Q3aii_R_L", "Q3aii_t_rise", "Q3aii_t_rise_modifier", "Q3aii_V_DC", "q3aii_v_pp"]}, {"name": "Q3d", "variables": ["Q3c_R_L", "Q3c_C1", "Q3c_V_S", "Q3c_Z_BDV"]}, {"name": "Q4d", "variables": ["Q3d_C1", "Q3d_V_S", "Q3d_L1", "Q3d_R_L"]}], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"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><strong>Part a) Signal Waveforms</strong></p>\n<p>Draw or derive the voltage and current wave forms for the following:</p>\n<table width=\"919\" height=\"317\" style=\"height: 472px; width: 634px; border-style: solid; border-color: #000000;\">\n<tbody>\n<tr style=\"height: 33px; background-color: #c2c0c0; text-align: center;\">\n<td style=\"width: 84.25px; height: 33px; border-style: solid; border-color: #000000; background-color: #b5b5b5; vertical-align: middle; text-align: center;\">Waveform</td>\n<td style=\"width: 206.458px; height: 33px; border-style: solid; border-color: #000000; background-color: #b5b5b5; vertical-align: middle; text-align: center;\">\n<p>Varibles</p>\n</td>\n<td style=\"width: 292.958px; height: 33px; border-style: solid; border-color: #000000; background-color: #b5b5b5; vertical-align: middle; text-align: center;\">\n<p>Circuit</p>\n</td>\n</tr>\n<tr style=\"height: 247px;\">\n<td style=\"width: 84.25px; height: 247px; border-style: solid; border-color: #000000; text-align: left;\">i. Sinusoidal&nbsp;</td>\n<td style=\"width: 206.458px; height: 247px; border-style: solid; border-color: #000000; text-align: left;\">\n<p>R<sub>L</sub>: {Q3ai_R_L} &Omega;</p>\n<p>Frequency (f<sub>s</sub>): {Q3ai_F_S} Hz</p>\n<p>V<sub>P-P: </sub>{Q3ai_V_PP} V</p>\n<p>DC Offset (V<sub>DC</sub>): {Q3ai_V_DC} V</p>\n</td>\n<td style=\"width: 292.958px; height: 247px; border-style: solid; border-color: #000000; text-align: center;\">\n<p></p>\n<p><img src=\"resources/question-resources/SbE_CC1_Q3ai.png\" alt=\"Simple Resistive Circuit\" width=\"221\" height=\"174\" style=\"display: block; margin-left: auto; margin-right: auto;\"/></p>\n</td>\n</tr>\n<tr style=\"height: 192px;\">\n<td style=\"width: 84.25px; border-style: solid; border-color: #000000; height: 192px; text-align: left;\">ii. Triangular</td>\n<td style=\"width: 206.458px; border-style: solid; border-color: #000000; height: 192px; text-align: left;\">\n<p>R<sub>L</sub>: {Q3aii_R_L/1000} k&Omega;</p>\n<p>Frequency (f<sub>s</sub>): {Q3aii_F_S} Hz</p>\n<p>V<sub>P-P: </sub>{Q3aii_V_PP} V</p>\n<p>DC Offset (V<sub>DC</sub>): {Q3aii_V_DC} V</p>\n<p>t<sub>Rise</sub>: {Q3aii_t_rise*1000} ms</p>\n</td>\n<td style=\"width: 292.958px; border-style: solid; border-color: #000000; height: 192px; text-align: center;\">\n<p style=\"text-align: center;\"><img src=\"resources/question-resources/SbE_CC1_Q3ai.png\" alt=\"Simple Resistive Circuit\" width=\"220\" height=\"173\"/></p>\n</td>\n</tr>\n</tbody>\n</table>\n<p></p>\n<p>SPICE Circuit suitable for analysis: <a href=\"https://www.multisim.com/content/5AuzGdcfbsojg9sJUUrxs9/sbe-cc1-q3a/open/\">SbE CC1 Q3a (multisim.com)</a></p>\n<p></p>\n<p><strong>[4Marks]</strong></p>"}, {"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><strong>Part b) Power Calculation</strong></p>\n<p>The figure shows a resistor network connected to a Triangular Waveform source and the equations that can be used to convert between Star and Delta impedance configurations:</p>\n<p><img src=\"resources/question-resources/SbE_CC1_Q3b.png\" alt=\"Resistor Network and Star-Delta Conversion Equations\" width=\"832\" height=\"462\"/></p>\n<p><strong>Circuit Varibles:</strong>&nbsp;V<sub>S(peak)</sub> = {Q3b_VS}V, f = {100}Hz t<sub>rise</sub> = {2}ms Hz, R<sub>1</sub>= {siground(dec(Q3b_R1/1000),2)}k&Omega;, R<sub>2</sub>= {siground(dec(Q3b_R2/1000),2)}k&Omega;, R<sub>3</sub>= {siground(dec(Q3b_R3/1000),2)}k&Omega;, R<sub>4</sub>= {siground(dec(Q3b_R4/1000),2)}k&Omega;</p>\n<p>For the values given, calculate or determine the RMS power dissipated in the whole circuit and resistor R&shy;<sub>1</sub>.&nbsp;</p>\n<p>SPICE Circuit Suitable for Analysis: <a href=\"https://www.multisim.com/content/cxrRsYAn36cgH8tuXAD4fo/sbe-cc1-q3b/open/\">*SbE CC1 Q3b (multisim.com)</a></p>\n<p><strong>[6Marks]</strong></p>\n<p></p>"}, {"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><strong>Part c) Power Supply</strong></p>\n<p>The figure shows a circuit designed for Voltage Reduction, Rectification and Regulation of an AC power source.&nbsp;</p>\n<p><img src=\"resources/question-resources/SbE_CC1_Q3c.png\" width=\"1001\" height=\"319\" style=\"display: block; margin-left: auto; margin-right: auto;\"/></p>\n<p style=\"text-align: left;\"><strong>Circuit Variables: </strong>V<sub>S</sub> = {Q3c_V_S}V<sub>RMS</sub>; C<sub>1</sub> = {Q3c_C1}mF; R<sub>1</sub>={1}&Omega;; R<sub>L</sub> = {Q3c_R_L}k&Omega;; T<sub>1</sub>: Turns on Primary Winding, &nbsp;N<sub>P</sub> = 20 and Secondary N<sub>S</sub> = 9;&nbsp; Diodes D<sub>1</sub> &amp; D<sub>2</sub>, Forward Bias Voltage = 860mV; Diode Z<sub>1</sub>, Reverse Breakdown Voltage = {Q3c_Z_BDV}V.&nbsp;&nbsp;</p>\n<p>For the component values given, explain how the circuit operates.&nbsp; Ensure that you:</p>\n<ul>\n<li style=\"list-style-type: none;\">\n<ul>\n<li>Draw or derive the wave forms expected/observed at each of the stages (A, B C &amp; D).</li>\n<li>Explain why the wave form changes as it does and what role the components have and why they might have been chosen.</li>\n<li>Calculate or derive the power consumed by the load.</li>\n</ul>\n</li>\n</ul>\n<p>SPICE Circuit Suitable for Analysis: <a href=\"https://www.multisim.com/content/oXq3s7yv8LnVdt6omUp2NP/sbe-cc1-el-q3c/open/\">SbE CC1 EL Q3c (multisim.com)</a></p>\n<p><strong>[8 Marks]</strong></p>"}, {"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><strong>Part d) Frequency Response</strong></p>\n<p>The circuit shown has a capacitor and inductor in parallel which has been designed to be in resonance at a known frequency.&nbsp; The signal is measured across the load (R<sub>L</sub>).</p>\n<p style=\"text-align: center;\"></p>\n<p style=\"text-align: center;\"><img src=\"resources/question-resources/SbE_CC1_Q3d.png\" width=\"548\" height=\"289\" style=\"display: block; margin-left: auto; margin-right: auto;\"/></p>\n<p style=\"text-align: left;\"><strong>Circuit Varibles:</strong> V<sub>S</sub> = {Q3d_V_S}V<sub>(RMS) </sub>, R<sub>L</sub> = {Q3d_R_L} k&Omega;<sub> </sub>C<sub>1</sub> = {Q3d_C1}&mu;F L<sub>1 </sub>= {Q3d_L1} mH</p>\n<p style=\"text-align: left;\">Using calculation or simulation, evaluate the performance of the circuit in a frequency range from 1Hz to 10kHz.&nbsp; Ensure that you:</p>\n<ul>\n<li>Explain what is meant by the term resonance and what role does it play in the circuit.</li>\n<li>Calculate or determine the frequency that the circuit will be in resonance.</li>\n<li>Plot and discuss the voltage relationship across the capacitor/inductor and the voltage across the load (R<sub>L</sub>).</li>\n<li>Discuss what application this type of circuit is useful for.</li>\n</ul>\n<p>SPICE Circuit Suitable for Analysis: <a href=\"https://www.multisim.com/content/KU6SMhmwZNVMdTVdsz6Liq/sbe-cc1-q3d/open/\" target=\"_blank\" rel=\"noopener\">*SbE CC1 Q3d (multisim.com)</a></p>\n<p></p>\n<p><strong>[12 Marks]</strong></p>"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "question", "contributors": [{"name": "Robert Bauld", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/19446/"}]}]}], "contributors": [{"name": "Robert Bauld", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/19446/"}]}