In `C - R` circuit, answer the following two questions
During charging of `C - R` circuit let `t_(1)` and `i_(1)` be the time constant and initial charging current when capacitor is assumed to be filled by a perfect insulator and `t_(2)` and `i_(2)` be the corresponding values when it is assumed imperfect. Then

Options

A. `t_(1) lt t_(2)`
B. `i_(1) gt i_(2)`
C. Both (a) and (b) are correct
D. Both (a) and (b) are wrong

Answer

To solve the problem regarding the charging of a capacitor in an RC circuit, we need to analyze the time constants and initial charging currents under two different assumptions about the capacitor's insulation.

### Step-by-Step Solution:

1. **Understanding Time Constant (τ)**:
- The time constant (τ) for an RC circuit is given by the formula:
\[ τ = R \cdot C \]
- Here, \(R\) is the resistance and \(C\) is the capacitance.

2. **Initial Charging Current (I)**:
- The initial charging current (\(I_0\)) can be calculated using Ohm's law:
\[ I_0 = \frac{E}{R} \]
- Where \(E\) is the electromotive force (EMF) of the circuit.

3. **Case 1: Perfect Insulator**:
- Let \(R_1\) be the resistance when the capacitor is assumed to be filled by a perfect insulator.
- The time constant and initial current in this case are:
\[ τ_1 = R_1 \cdot C \]
\[ I_1 = \frac{E}{R_1} \]

4. **Case 2: Imperfect Insulator**:
- Let \(R_2\) be the resistance when the capacitor is assumed to be filled by an imperfect insulator.
- Since the insulation is imperfect, we assume \(R_2 > R_1\).
- The time constant and initial current in this case are:
\[ τ_2 = R_2 \cdot C \]
\[ I_2 = \frac{E}{R_2} \]

5. **Comparing Time Constants**:
- Since \(R_2 > R_1\), we have:
\[ τ_2 = R_2 \cdot C > R_1 \cdot C = τ_1 \]
- Therefore, \(τ_2 > τ_1\).

6. **Comparing Initial Charging Currents**:
- Since \(R_2 > R_1\), we have:
\[ I_2 = \frac{E}{R_2} < \frac{E}{R_1} = I_1 \]
- Therefore, \(I_2 < I_1\).

7. **Conclusion**:
- We conclude that:
- The time constant when the capacitor is filled by an imperfect insulator is greater than that when filled by a perfect insulator: \(τ_2 > τ_1\).
- The initial charging current when the capacitor is filled by an imperfect insulator is less than that when filled by a perfect insulator: \(I_2 < I_1\).

### Final Answers:
- \(τ_2 > τ_1\) (Time constant is greater for imperfect insulation)
- \(I_2 < I_1\) (Initial charging current is less for imperfect insulation)