An a.c. voltage is applied to a resistance R and inductance L in series. The phase difference between the applied voltage and the current in the circuit, if the resistance Rand inductive reactance are both equal to `5Omega` is:

Options

A. 0
B. `pi/6`
C. `pi/4`
D. `pi/2`

Explanation

To find the phase difference between the applied voltage and the current in a circuit with resistance \( R \) and inductance \( L \) in series, we can follow these steps:

### Step 1: Identify the given values
We are given:
- Resistance \( R = 5 \, \Omega \)
- Inductive reactance \( X_L = 5 \, \Omega \)

### Step 2: Use the formula for phase difference
The phase difference \( \phi \) between the voltage and the current in an R-L circuit is given by the formula:
\[ \tan \phi = \frac{X_L}{R} \]
where \( X_L \) is the inductive reactance and \( R \) is the resistance.

### Step 3: Substitute the values into the formula
Substituting the given values into the formula:
\[ \tan \phi = \frac{5}{5} = 1 \]

### Step 4: Calculate the phase angle
To find \( \phi \), we take the arctangent of both sides:
\[ \phi = \tan^{-1}(1) \]
The angle whose tangent is 1 is \( 45^\circ \) or \( \frac{\pi}{4} \) radians.

### Conclusion
Thus, the phase difference between the applied voltage and the current in the circuit is:
\[ \phi = \frac{\pi}{4} \text{ radians} \]