Question

A capacitor of capacitance $10\mu F$ is connected to a battery of emf $2V$. It is found that it takes $50ms$ for the charge on the capacitor to become $12.6\mu C$. Find the resistance of the circuit.

• A. $51k\Omega$
• B. $7k\Omega$
• C. $5k\Omega$
• D. $6k\Omega$

Answer 1

The correct option is C $5k\Omega$

We know,

$Q=Q_0(1-e^{\frac{-t}{\tau }})$

Where $Q_0=20\mu C$

For $Q=12.6\mu C$

$\frac{12.6}{20}=(1-e^{\frac{-t}{\tau }})$

$e^{\frac{-t}{\tau }}=0.37=e^{-1}$

Comparing,

$t=\tau =50\times {10}^{-3}$

$R\times 10\times {10}^{-6}=50\times {10}^{-3}$

$R=5\times {10}^3\Omega =5k\Omega$