Quick answer: Kirchhoff's junction rule conserves charge and his loop rule conserves energy, giving equations for every branch current. This AP Physics C test on RC circuits has 8 questions worth 20 marks, to do in 45 minutes: Kirchhoff’s rules, battery and load and charging a capacitor. The mark scheme is on a separate page; free printable PDF.
This test lasts 45 minutes and is marked out of 20. Show all steps, give answers with units, and also use full sentences for explanations. Take e⁻¹ = 0.368 and e⁻² = 0.135 where useful. Finally, you may use a calculator.
Level: AP Physics C (Mechanics and E&M, calculus-based) · Curriculum: AP PC:E&M Unit 11
Question 1 Kirchhoff’s rules (2 marks)
Firstly, state the physical principle behind (a) the junction rule and then (b) the loop rule.Question 2 Battery and load (2 marks)
A battery of emf 15 V and internal resistance 1.0 Ω drives a 4.0 Ω resistor, so calculate the current and then the terminal voltage.Question 3 Charging a capacitor (3 marks)
You close the switch in the circuit at t = 0 with the capacitor uncharged.Question 4 Discharge time (3 marks)
A 470 μF capacitor that starts at 12 V discharges through 1.0 kΩ. Then calculate how long the voltage takes to fall to 4.0 V.Question 5 Limits in time (2 marks)
Explain how an uncharged capacitor behaves immediately after you close the switch, and then after a very long time.Question 6 Derive the equation (3 marks)
First, use the loop rule for a charging RC circuit to write a differential equation for q(t). show that q = Cε(1 − e−t/RC) satisfies it.Question 7 Energy balance (3 marks)
A 100 μF capacitor charges to 6.0 V through a resistor from a 6.0 V battery. Therefore, calculate the energy supplied by the battery, stored in the capacitor and dissipated in the resistor.Question 8 Sketching the current (2 marks)
Sketch the current against time for a discharging capacitor, and then mark τ on the sketch.
