Question

Figure shows an uncharged capacitor connected in series with a resistor $R$ and ideal battery. At $t=0$ switch $S_w$ is closed and it is observed that when charge on capacitor is $75$$\%$ of maximum value then current in the circuit is $1A$, then value of $R$ is :

• A. 1 $\Omega$
• B. 10 $\Omega$
• C. 5 $\Omega$
• D. can't be determined

Answer 1

Answer: (C)

5 $\Omega$

Charge on capacitor at some time t is $Q=Q_0[1-e^{\frac{-t}{RC}}]$

$\Rightarrow 0.75Q_0=Q_0[1-e^{\frac{-t}{RC}}]$

$\Rightarrow 0.25=e^{\frac{-t}{RC}}$ (i)

$Q_0=C{V}_0=20\mu C$

At this point of time, current in the circuit $I=\frac{dQ}{dt}=\frac{Q_0}{RC}{e}^{\frac{-t}{RC}}$

$\Rightarrow 1=\frac{20}{R}{e}^{\frac{-t}{RC}}$(ii)

Using (i) and(ii)

$1=\frac{20}{R}\left(0.25\right)$

$R=5\Omega$