The charging current for a capacitor is 1 A, then the displacement current is

Options

A. ` 1 A`
B. `0 A`
C. `2 A`
D. `(1)/(2) A`

Answer

To solve the problem regarding the displacement current when the charging current for a capacitor is given as 1 A, we can follow these steps:

### Step-by-Step Solution

1. **Understanding the Concept**:
The displacement current \( I_d \) is related to the changing electric field in a capacitor. 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.

2. **Electric Flux Calculation**:
The electric flux \( \Phi_E \) through the capacitor is given by:
\[ \Phi_E = E \cdot A \]
where \( E \) is the electric field between the plates and \( A \) is the area of the plates. For parallel plates, the angle between the electric field and the area vector is 0 degrees, hence \( \cos(0) = 1 \).

3. **Electric Field in a Capacitor**:
The electric field \( E \) between the plates of a parallel plate capacitor can be expressed as:
\[ E = \frac{Q}{\epsilon_0 A} \]
where \( Q \) is the charge on the plates.

4. **Substituting into Flux**:
Substituting the expression for \( E \) into the flux equation gives:
\[ \Phi_E = \left(\frac{Q}{\epsilon_0 A}\right) A = \frac{Q}{\epsilon_0} \]

5. **Differentiating the Flux**:
Now, we differentiate the electric flux with respect to time:
\[ \frac{d\Phi_E}{dt} = \frac{d}{dt}\left(\frac{Q}{\epsilon_0}\right) = \frac{1}{\epsilon_0} \frac{dQ}{dt} \]

6. **Substituting into Displacement Current**:
Now substituting this back into the equation for displacement current:
\[ I_d = \epsilon_0 \frac{d\Phi_E}{dt} = \epsilon_0 \cdot \frac{1}{\epsilon_0} \frac{dQ}{dt} = \frac{dQ}{dt} \]

7. **Relating to Conduction Current**:
The conduction current \( I_c \) is defined as:
\[ I_c = \frac{dQ}{dt} \]
Given that the charging current is 1 A, we have:
\[ I_c = 1 \, \text{A} \]

8. **Final Result**:
Therefore, the displacement current \( I_d \) is equal to the conduction current:
\[ I_d = I_c = 1 \, \text{A} \]

### Conclusion
The displacement current when the charging current for a capacitor is 1 A is also 1 A.

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