Question

A battery of EMF E, resistance R and an uncharged capacitor C are connected in the circuit as shown in figure. Then after switch is turned on :

• A. Current through R and charge on capacitor C both will increase with time.
• B. Current through R and charge on capacitor C both will decrease with time.
• C. Current through R will increase but charge on C will decrease with time.
• D. Current through R will decrease but charge on C will increase with time.

Answer 1

Answer: (D)

Current through R will decrease but charge on C will increase with time.

When the switch is turned on the capacitor will start charging. The equation of charging is

$Q\left(t\right)=Q_0(1-e^{-t/CR})$ and current through R is

$I=\frac{dQ}{dt}=\frac{Q_0}{CR}{e}^{-t/CR}$

From this equation we can say that current through R will decrease but charge on C will increase with time.