Voltage across an inductor, capacitor and a resistor is 30 V, 0 V and 60 V respectively in a series LCR circuit then the phase difference between the applied voltage and applied current will be:

Options

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

Explanation

To find the phase difference between the applied voltage and the applied current in a series LCR circuit, we can use the following steps:

### Step 1: Identify the given voltages
We are given the voltages across the inductor (V_L), capacitor (V_C), and resistor (V_R):
- Voltage across the inductor, V_L = 30 V
- Voltage across the capacitor, V_C = 0 V
- Voltage across the resistor, V_R = 60 V

### Step 2: Calculate the net voltage across the inductor and capacitor
In a series LCR circuit, the net voltage across the inductor and capacitor can be calculated as:
\[ V_{LC} = V_L - V_C \]
Substituting the values:
\[ V_{LC} = 30 V - 0 V = 30 V \]

### Step 3: Use the formula for phase difference
The phase difference (φ) between the applied voltage (V) and the current (I) in an LCR circuit can be calculated using the formula:
\[ \tan(\phi) = \frac{V_{LC}}{V_R} \]
Where:
- \( V_{LC} \) is the net voltage across the inductor and capacitor
- \( V_R \) is the voltage across the resistor

Substituting the values:
\[ \tan(\phi) = \frac{30 V}{60 V} = \frac{1}{2} \]

### Step 4: Calculate the phase difference
To find φ, we take the arctan of both sides:
\[ \phi = \tan^{-1}\left(\frac{1}{2}\right) \]

### Step 5: Use a calculator to find the angle
Using a calculator, we find:
\[ \phi \approx 26.57^\circ \]

### Final Answer
The phase difference between the applied voltage and the applied current is approximately \( 26.57^\circ \).

---