Question

A parallel plate capacitor has plates of unequal area. Smaller plate is connected to the positive terminal of the battery and the larger plate is connected to its negative terminal. Let $Q_p$ and $Q_n$ be the charges appearing on the positive and negative plates respectively. Then

• A. $Q_p>Q_n$
  
• B. $Q_p<Q_n$
  
• C. $Q_p=Q_n$
  
• D. Data insufficient

Answer 1

The correct option is C $Q_p=Q_n$


The charge induced on the plates of the capacitor is independent of the area of the plates.

As, we know that, $Q=CV$ where, $C$ is constant of proportionality. Since the plates are connected to the same battery, the potential difference $V$ across them would be constant.

So, the charges which will reside on the inner surfaces of the two plates will be equal in magnitude and opposite in nature due to induction.

Therefore in this case $\left|Q_p\right|=\left|Q_n\right|$.

Hence, option (c) is the correct answer.

Key concept: Charges on the two surfaces of the conductor plates placed really close and facing each other will be equal and opposite.