The displacement current flows in the dielectric of a capacitor when the potential difference across its plates-

Options

A. Maximum
B. Zero
C. Minimum
D. Varying

Answer

To solve the problem regarding the displacement current that flows in the dielectric of a capacitor when a potential difference is applied across its plates, we can follow these steps:

### Step 1: Understand the Concept of Displacement Current
Displacement current is a concept introduced by James Clerk Maxwell to account for the changing electric field in a dielectric medium when a capacitor is charged. It is defined as the rate of change of electric displacement field (D) with respect to time.

### Step 2: Identify the Components of the Capacitor
A capacitor consists of two plates separated by a dielectric material. When a potential difference (V) is applied across the plates, an electric field is established in the dielectric.

### Step 3: Apply the Formula for Displacement Current
The displacement current (ID) can be expressed mathematically as:
\[ I_D = \epsilon_0 \frac{dE}{dt} A \]
where:
- \( I_D \) is the displacement current,
- \( \epsilon_0 \) is the permittivity of free space,
- \( E \) is the electric field in the dielectric,
- \( A \) is the area of the plates.

### Step 4: Relate Displacement Current to Conduction Current
The displacement current can also be related to the conduction current (Ic) flowing through the circuit. The relationship can be expressed as:
\[ I_D = I_C \]
where \( I_C \) is the conduction current.

### Step 5: Analyze the Time Dependence of Displacement Current
As the capacitor charges, the conduction current decreases over time, which affects the displacement current. The displacement current can be expressed as:
\[ I_D = I \cdot e^{-t/\tau} \]
where \( \tau \) is the time constant of the RC circuit.

### Step 6: Conclusion on the Behavior of Displacement Current
- At \( t = 0 \), the displacement current is maximum, equal to the conduction current \( I \).
- As time increases, the displacement current decreases exponentially.
- The potential difference across the capacitor plates also varies as the displacement current changes.

### Final Answer
The displacement current flows in the dielectric of a capacitor when the potential difference across its plates is applied and varies over time as the capacitor charges.

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