An RL circuit is connected to 12m V , 30 Hz AC supply . The voltage leads the current by `60^(@)` . Calculate the value of R and L if current flowing in the circuit is 0.5 A .

Answer

To solve the problem step by step, we will use the information given about the RL circuit connected to a 12V, 30Hz AC supply, where the voltage leads the current by 60°. We need to calculate the values of resistance (R) and inductance (L) given that the current flowing in the circuit is 0.5 A.

### Step-by-Step Solution:

1. **Identify Given Values:**
- RMS Voltage (V) = 12 V
- Frequency (f) = 30 Hz
- Current (I) = 0.5 A
- Phase angle (φ) = 60°

2. **Calculate Voltage Across Resistance (Vr):**
- The voltage across the resistance can be calculated using the formula:
\[ V_r = V \cos(φ) \]
- Substitute the values:
\[ V_r = 12 \cos(60°) = 12 \times \frac{1}{2} = 6 \, \text{V} \]

3. **Calculate Resistance (R):**
- Using Ohm's Law, we can find the resistance:
\[ R = \frac{V_r}{I} \]
- Substitute the values:
\[ R = \frac{6 \, \text{V}}{0.5 \, \text{A}} = 12 \, \Omega \]

4. **Calculate Voltage Across Inductance (Vl):**
- The voltage across the inductance can be calculated using the formula:
\[ V_l = V \sin(φ) \]
- Substitute the values:
\[ V_l = 12 \sin(60°) = 12 \times \frac{\sqrt{3}}{2} = 6\sqrt{3} \approx 10.392 \, \text{V} \]

5. **Calculate Inductive Reactance (XL):**
- The inductive reactance can be expressed as:
\[ V_l = I \cdot X_L \]
- Rearranging gives:
\[ X_L = \frac{V_l}{I} \]
- Substitute the values:
\[ X_L = \frac{10.392 \, \text{V}}{0.5 \, \text{A}} = 20.784 \, \Omega \]

6. **Calculate Inductance (L):**
- The inductive reactance is also given by:
\[ X_L = 2 \pi f L \]
- Rearranging gives:
\[ L = \frac{X_L}{2 \pi f} \]
- Substitute the values:
\[ L = \frac{20.784}{2 \pi \times 30} = \frac{20.784}{188.4} \approx 0.110 \, \text{H} \]
- Converting to milliHenries:
\[ L \approx 110 \, \text{mH} \]

### Final Answers:
- Resistance (R) = 12 Ω
- Inductance (L) = 110 mH