Question

27.3 An uncharged capacitor and a resistor are connected in series of source of emf. If emf is 9.00 V, C=20.0 uF, and R=100 Ohms (a) find the time constant of the circuit, (b) the maximum charge on the capacitor, and (c) the charge on the capacitor at a time equal to one time constant after the battery is connected.

Answer 1

a)

$$\tau=RC=(100)(20\cdot 10^{-6})=0.002\ s$$

b)

$$Q=CU=(20\cdot 10^{-6})(9)=1.80\cdot 10^{-4}C$$

c)

$$q=Q\left(1-e^{-\frac{\tau}{\tau}}\right)=Q\left(1-e^{-1}\right)$$

$$q=1.8\cdot 10^{-4}\left(1-e^{-1}\right)=1.14\cdot 10^{-4}C$$