A capacitor C is connected in series with a resistor R across a battery and an open switch. If a second capacitor of capacitance 2C is connected in series to the first, the time constant of the new RC circuit will be
A) the same as before.
B) larger than before.
C) smaller than before.
D) variable.

Question

Quizplus · Accepted Answer

When two capacitors are connected in series, the effective capacitance is given by:
$$C_{eff} = \frac{C_1 C_2}{C_1 + C_2}$$
In this case, when the second capacitor of capacitance 2C is connected in series to the first, the effective capacitance becomes:
$$C_{eff} = \frac{C(2C)}{C+2C} = \frac{2}{3}C$$
Now, the time constant of the new RC circuit is given by:
$$	au' = RC_{eff} = R\frac{2}{3}C$$
This is smaller than the original time constant of RC, which was given by:
$$	au = RC$$
Therefore, the correct answer is (C) smaller than before.

A Capacitor C Is Connected in Series with a Resistor