The charging current for a capacitor is 0.5A. What is the displacement current across its plates?

Options

A. 0.25 A
B. 0.5 A
C. 0.75 A
D. 1.5 A

Explanation

To find the displacement current across the plates of a capacitor when the charging current is given, we can follow these steps:

### Step 1: Understand the Concept of Displacement Current
The 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:
\[ I_d = \epsilon_0 \frac{d\Phi_E}{dt} \]
where \( \Phi_E \) is the electric flux, and \( \epsilon_0 \) is the permittivity of free space.

### Step 2: Relate Charging Current to Displacement Current
In a capacitor, the total current \( I \) flowing into the capacitor is the sum of the conduction current \( I_C \) and the displacement current \( I_d \):
\[ I = I_C + I_d \]
For a capacitor, the conduction current \( I_C \) is essentially the charging current, which is given in the problem.

### Step 3: Set the Given Values
From the problem, we know that the charging current \( I_C \) is 0.5 A. Therefore, we can write:
\[ I_C = 0.5 \, \text{A} \]

### Step 4: Apply the Relationship
Since the conduction current \( I_C \) is equal to the displacement current \( I_d \) when the capacitor is charging (because there is no conduction current through the dielectric), we can say:
\[ I_d = I_C \]

### Step 5: Calculate the Displacement Current
Substituting the value of the conduction current into the equation gives:
\[ I_d = 0.5 \, \text{A} \]

### Conclusion
Thus, the displacement current across the plates of the capacitor is:
\[ I_d = 0.5 \, \text{A} \]

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