Question

A capacitor C1 =1F is connected to a 1V battery using a wire with a total resistance R = 1Ohm.

Suppose after the charging is complete the capacitor C1 is connected to another capacitor C2 = 2 F using a wire with a total resistance of R =0.3 Ohm. Now the first capacitor discharges while the second one charges.

Let’s derive the differential equation describing the discharge in this 2-capacitor circuit. Let’s label the charge on the capacitor C1 as q1(t) and the charge on the capacitor C2 as q2(t).

2.10 [1pt] Sketch the circuit diagram, label the charges and their signs at the capacitors plate, and link q1(t) and q2(t).

Hint, what is q1(t=0) and q2(t=0) (t=0 is the instant the connection was made)?

ANSWER

2.11 [1pt] Express the current through the resistor in terms of the charge derivative and write down the voltages across both capacitors and the resistor add up to zero. From the resulting equation, deduce the characteristic charging time without solving it.

ANSWER

Answer 1

The solution of the problem is given below