Two identical capacitors A and B are charged to the same potential and then made to discharge through resistances `R_(A)` and `R_(B)` respectively, with `R_(A) gt R_(B)`.

Options

A. A will require greater time than B to discharge
B. More heat will be produced in A than in B.
C. More heat will be produced in B than in A.
D. A will require less time than B to discharge completely

Answer

To solve the problem, let's analyze the situation step by step.

### Step 1: Understand the scenario
We have two identical capacitors, A and B, which are charged to the same potential. They are then discharged through resistances \( R_A \) and \( R_B \) respectively, where \( R_A > R_B \).

### Step 2: Determine the time constant for each capacitor
The time constant \( \tau \) for a capacitor discharging through a resistor is given by the formula:
\[ \tau = R \cdot C \]
where \( R \) is the resistance and \( C \) is the capacitance of the capacitor. Since both capacitors are identical, they have the same capacitance \( C \).

For capacitor A:
\[ \tau_A = R_A \cdot C \]
For capacitor B:
\[ \tau_B = R_B \cdot C \]

### Step 3: Compare the time constants
Since \( R_A > R_B \), it follows that:
\[ \tau_A > \tau_B \]
This means that capacitor A will take longer to discharge compared to capacitor B.

### Step 4: Analyze the heat produced
The energy stored in a capacitor is given by:
\[ E = \frac{1}{2} C V^2 \]
Since both capacitors are charged to the same potential \( V \) and have the same capacitance \( C \), the energy stored in both capacitors is the same.

When the capacitors discharge, the energy is converted into heat. Therefore, the heat produced in both capacitors will also be the same.

### Step 5: Conclusion
Based on the analysis:
1. Capacitor A will require more time to discharge than capacitor B.
2. The heat produced in both capacitors will be the same.

### Final Answers:
- A will require greater time than B to discharge (Correct).
- More heat will be produced in A than in B (Incorrect).
- More heat will be produced in B than in A (Incorrect).
- A will require less time than B to discharge completely (Incorrect).