Instantaneous displacement current of `1.0` A in the space between the paraller plates of `1 mu F` capacitor can be established by changing potenial difference of:

Options

A. `10^(-6) V//s`
B. `10^(6) V//s`
C. `10^(-8) V//s`
D. `10^(8) V//s`

Explanation

To solve the problem, we need to find the potential difference that can establish an instantaneous displacement current of 1.0 A in the space between the parallel plates of a 1 µF capacitor.

### Step-by-Step Solution:

1. **Understand the Concept of Displacement Current**:
The displacement current (I_d) in a capacitor can be expressed using the formula:
\[ I_d = C \frac{dV}{dt} \]
where:
- \( I_d \) is the displacement current,
- \( C \) is the capacitance,
- \( \frac{dV}{dt} \) is the rate of change of potential difference.

2. **Identify Given Values**:
From the problem, we know:
- Displacement current, \( I_d = 1.0 \, \text{A} \)
- Capacitance, \( C = 1 \, \mu\text{F} = 1 \times 10^{-6} \, \text{F} \)

3. **Rearranging the Formula**:
We need to find the rate of change of potential difference \( \frac{dV}{dt} \). Rearranging the formula gives us:
\[ \frac{dV}{dt} = \frac{I_d}{C} \]

4. **Substituting the Values**:
Now, substituting the known values into the equation:
\[ \frac{dV}{dt} = \frac{1.0 \, \text{A}}{1 \times 10^{-6} \, \text{F}} = 1.0 \times 10^{6} \, \text{V/s} \]

5. **Conclusion**:
The instantaneous change in potential difference per unit time is \( 10^{6} \, \text{V/s} \). Therefore, the potential difference can be established by changing the potential difference at a rate of \( 10^{6} \, \text{V/s} \).

### Final Answer:
The potential difference can be established by changing the potential difference at a rate of \( 10^{6} \, \text{V/s} \).

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