Two part question, student has to rearrange the parallel resistors formula (stated in the question) to make L_1 or L_2 the subject (variable is chosen randomly), then find the value of this variable when values of the other variables in the formula are given. These values are randomly chosen.
\nNote that the advice for this question has two versions, the one displayed to the student depends on which variable is selected by the question.
", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "When two electrical resistors of magnitudes \\(R_1\\) and \\(R_2\\) respectively are connected in parallel the total effective resistance \\(R\\) is given by the formula \\[R=\\frac{R_1R_2}{R_1+R_2}.\\]
", "advice": "We have
\n\\begin{align}R&=\\frac{R_1R_2}{R_1+R_2}\\quad\\text{multiply both sides by }R_1+R_2\\\\R(R_1+R_2)&=R_1R_2\\quad\\text{expand the brackets}\\\\RR_1+RR_2&=R_1R_2\\quad\\text{subtract }RR_1\\text{ from both sides}\\\\RR_2&=R_1R_2-RR_1\\quad\\text{factorise RHS}\\\\RR_2&=R_1(R_2-R)\\quad\\text{divide both sides by } (R_2-R)\\\\R_1&=\\frac{RR_2}{R_2-R}\\end{align}
\n\\begin{align}R&=\\frac{R_1R_2}{R_1+R_2}\\quad\\text{multiply both sides by }R_1+R_2\\\\R(R_1+R_2)&=R_1R_2\\quad\\text{expand the brackets}\\\\RR_1+RR_2&=R_1R_2\\quad\\text{subtract }RR_2\\text{ from both sides}\\\\RR_1&=R_1R_2-RR_2\\quad\\text{factorise RHS}\\\\RR_1&=R_2(R_1-R)\\quad\\text{divide both sides by } (R_1-R)\\\\R_2&=\\frac{RR_1}{R_1-R}\\end{align}
\nGiven \\(R=\\var{L}\\) ohms and \\(\\var{other_var}=\\var{L1}\\) ohms we have
\n\\begin{align}R_1&=\\frac{RR_2}{R_2-R}\\\\&=\\frac{\\var{L}\\times\\var{L1}}{\\var{L1}-\\var{L}}\\\\&\\approx\\var{precround({L}*{L1}/({L1}-{L}),2)}\\text{ ohms}\\end{align}
\n\\begin{align}R_2&=\\frac{RR_1}{R_1-R}\\\\&=\\frac{\\var{L}\\times\\var{L1}}{\\var{L1}-\\var{L}}\\\\&\\approx\\var{precround({L}*{L1}/({L1}-{L}),2)}\\text{ ohms}\\end{align}
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", "templateType": "anything", "can_override": false}, "ans": {"name": "ans", "group": "Ungrouped variables", "definition": "answers[select]", "description": "correct formula for the variable selected by select
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\\(\\var{sel_var}=\\)[[0]] (You must show full working on your ahndwriten working for this part to get full marks)
\nIf \\(R=\\var{L}\\) ohms and \\(\\var{other_var}=\\var{L1}\\) ohms, what is the value of \\(\\var{sel_var}\\)?
\n\\(\\var{sel_var}=\\)[[1]] ohms (answer to 2 decimal places)
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