Displacement current is maximum during charging of capacitor. When charge on the capacitor is

Options

A. Maximum
B. Minimum
C. Any value of charge
D. Depends on nature of capacitor

Answer

To solve the question regarding when the displacement current is maximum during the charging of a capacitor, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Displacement Current**: Displacement current is a concept introduced by James Clerk Maxwell to account for the changing electric field in regions where there is no conduction current. It is defined as \( I_d = \epsilon_0 \frac{dE}{dt} \), where \( \epsilon_0 \) is the permittivity of free space and \( \frac{dE}{dt} \) is the rate of change of the electric field.

2. **Charging of a Capacitor**: When a capacitor is being charged, the charge \( q \) on the capacitor plates increases over time. The electric field \( E \) between the plates of the capacitor is related to the charge by the formula \( E = \frac{\sigma}{\epsilon_0} = \frac{q}{A \epsilon_0} \), where \( A \) is the area of the plates.

3. **Rate of Change of Charge**: The current \( I \) flowing into the capacitor is given by \( I = \frac{dq}{dt} \). During the charging process, this current is at its maximum when the capacitor is initially uncharged (i.e., when it starts charging from zero).

4. **Relationship Between Displacement Current and Charge**: The displacement current \( I_d \) is directly proportional to the rate of change of charge \( \frac{dq}{dt} \). Thus, \( I_d \) will also be maximum when \( \frac{dq}{dt} \) is maximum.

5. **Condition of Charge on Capacitor**: The charge on the capacitor is minimum (zero) at the beginning of the charging process. As the capacitor charges, the rate of change of charge decreases until the capacitor is fully charged, at which point \( \frac{dq}{dt} = 0 \).

6. **Conclusion**: Therefore, the displacement current is maximum during the charging of a capacitor when the charge on the capacitor is at its minimum (zero).

### Final Answer:
The displacement current is maximum during the charging of a capacitor when the charge on the capacitor is **minimum**.

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