Answer to Question #306352 in Physics for mcc

Question

A 2μF and 6μF capacitor are connected in series with a 12V battery. What is the maximum charge stored on the 2μF capacitor?

a. 96μC

c. 18μC

b. 13.5μC

d. 24μC

Answer 1

Since the capacitors in series have the same charging current flowing through them, their charges must be equal (see https://opentextbc.ca/universityphysicsv2openstax/chapter/capacitors-in-series-and-in-parallel/). The equivalent capacitance $C$ of the system can be found as follows:

$$\dfrac{1}{C} = \dfrac{1}{C_1} + \dfrac{1}{C_2}$$

where $C_1 = 2\times 10^{-6}F, C_2 = 6\times 10^{-6}F$.

Thus, obtain:

$$\dfrac{1}{C} = \dfrac{1}{2\times 10^{-6}F} + \dfrac{1}{6\times 10^{-6}F}\\ C = 1.5\times 10^{-6}F$$

The charge is given then:

$$Q = CV = 1.5\times10^{-6}F\cdot 12V = 18\times 10^{-6}C$$

Answer. c.