Question

A capacitor of capacitance $C$ is charged to a potential difference $V$ and then connected in series with an open key and a pure resistor $R$ . At time $t=0$ , the key is closed. If $I$ is current at time $t=0$ , a plot of $logI$ against $t$ is shown in the graph $(2)$ . Later one of the parameters, i.e., $V$ , $R$ and $C$ is changed, keeping the other two constant and graph $(2)$ is recorded. Then

• A. $C$ is reduced
• B. $C$ is increased
• C. $R$ is reduced
• D. $R$ is increased

Answer 1

Answer: (B)

During discharging of a capacitor, the current is given by,
$I=\frac{E}{R}{e}^{-\frac{t}{RC}}$
$\log I=\log \frac{E}{R}{e}^{-\frac{t}{RC}}$
$\log I=-\frac{t}{RC}+\log \frac{E}{R}$
Intercept is constant $\Rightarrow$ $E$ & $R$ constant
Magnitude of slope decreases $\Rightarrow$ $C$ is increased