the resistance and inductance of series circuit are `5Omega` and `20H` respectively. At the instant of closing the switch, the current is increasing at the rate `4A-s`. The supply voltage is

Options

A. 20 V
B. 80 V
C. 120 V
D. 100 V

Explanation

To solve the problem, we need to determine the supply voltage in a series circuit with given resistance and inductance, where the current is increasing at a specific rate at the moment the switch is closed.

### Step-by-Step Solution:

1. **Identify Given Values:**
- Resistance (R) = 5 Ω
- Inductance (L) = 20 H
- Rate of change of current (di/dt) = 4 A/s

2. **Calculate the Voltage across the Inductor:**
The voltage across the inductor (V_L) can be calculated using the formula:
\[ V_L = L \cdot \frac{di}{dt} \]
Substituting the known values:
\[ V_L = 20 \, \text{H} \cdot 4 \, \text{A/s} = 80 \, \text{V} \]

3. **Determine the Total Voltage Supply:**
At the instant the switch is closed, the entire supply voltage (V) is equal to the voltage across the inductor, since the current has not yet reached a steady state and there is no voltage drop across the resistor at that moment.
Therefore, the supply voltage is:
\[ V = V_L = 80 \, \text{V} \]

4. **Conclusion:**
The supply voltage at the instant of closing the switch is 80 V.

### Final Answer:
The supply voltage is **80 V**.

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