In a series `L-R` circuit, connected with a sinusoidal ac source, the maximum potential difference acrosssd `L` and `R` are respectively 3 volts and 4 volts
If the current at this instant is decreasing the magnitude of potential difference at that instant across the ac source is

Options

A. Increasing
B. Decreasing
C. Constant
D. Cannot be said

Answer

To solve the problem, we need to analyze the behavior of the potential differences in a series L-R circuit connected to an AC source. Given that the maximum potential differences across the inductor (L) and the resistor (R) are 3 volts and 4 volts respectively, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Values**:
- Maximum potential difference across the inductor, \( V_L = 3 \, \text{V} \)
- Maximum potential difference across the resistor, \( V_R = 4 \, \text{V} \)

2. **Understand the Circuit Behavior**:
- In a series L-R circuit connected to an AC source, the total potential difference across the circuit is the vector sum of the potential differences across the inductor and the resistor.
- The potential difference across the inductor leads the current by 90 degrees, while the potential difference across the resistor is in phase with the current.

3. **Calculate the Total Maximum Potential Difference**:
- The total maximum potential difference \( V \) across the AC source can be calculated using the Pythagorean theorem:
\[ V = \sqrt{V_L^2 + V_R^2} \]
- Substituting the values:
\[ V = \sqrt{(3 \, \text{V})^2 + (4 \, \text{V})^2} = \sqrt{9 + 16} = \sqrt{25} = 5 \, \text{V} \]

4. **Consider the Current Behavior**:
- The problem states that the current at this instant is decreasing. This means that the rate of change of current \( \frac{dI}{dt} \) is negative.
- The potential difference across the inductor is given by \( V_L = L \frac{dI}{dt} \). Since \( \frac{dI}{dt} \) is negative, \( V_L \) will also be negative, indicating that the inductor is opposing the decrease in current.

5. **Determine the Instantaneous Voltage Across the AC Source**:
- Since the current is decreasing, the inductor's potential difference \( V_L \) will contribute positively to the total voltage across the AC source.
- Therefore, at this instant, the total potential difference across the AC source remains at its maximum value, which we calculated as 5 volts.

### Final Answer:
The magnitude of the potential difference at that instant across the AC source is **5 volts**.