In a series LCR circuit the voltage across an inductor, capacitor and resistor are 20 V, 20 V and 40 V respectively. The phase difference between the applied voltage and the current in the circuit is

Options

A. `30^(@)`
B. `45^(@)`
C. `60^(@)`
D. `0^(@)`

Explanation

To find the phase difference between the applied voltage and the current in a series LCR circuit where the voltages across the inductor (V_L), capacitor (V_C), and resistor (V_R) are given, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Voltage across the inductor, \( V_L = 20 \, V \)
- Voltage across the capacitor, \( V_C = 20 \, V \)
- Voltage across the resistor, \( V_R = 40 \, V \)

2. **Understand the Relationship in LCR Circuits:**
- In a series LCR circuit, the total voltage across the circuit is the vector sum of the voltages across the inductor, capacitor, and resistor.
- The phase difference \( \phi \) between the total voltage and the current can be calculated using the formula:
\[ \tan \phi = \frac{V_L - V_C}{V_R} \]

3. **Substitute the Values into the Formula:**
- Substitute the known values into the equation:
\[ \tan \phi = \frac{20 \, V - 20 \, V}{40 \, V} \]

4. **Calculate \( \tan \phi \):**
- Simplifying the equation gives:
\[ \tan \phi = \frac{0}{40} = 0 \]

5. **Determine the Phase Difference \( \phi \):**
- Since \( \tan \phi = 0 \), we know that:
\[ \phi = 0^\circ \]

6. **Conclusion:**
- The phase difference between the applied voltage and the current in the circuit is \( 0^\circ \).

### Final Answer:
The phase difference between the applied voltage and the current in the circuit is \( 0^\circ \).

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