An inductive circuit a resistance of `10ohm` and an inductance of `2.0` henry. If an AC voltage of `120`volt and frequency of `60Hz` is applied to this circuit, the current in the circuit would be nearly

Options

A. (a)`0.32` amp
B. (b)`0.16`amp
C. (c)048 amp
D. (d)`0.80`amp

Answer

To find the current in an inductive circuit with a given resistance and inductance when an AC voltage is applied, we can follow these steps:

### Step-by-Step Solution:

1. **Identify Given Values:**
- Resistance (R) = 10 ohms
- Inductance (L) = 2.0 henry
- AC Voltage (V) = 120 volts
- Frequency (f) = 60 Hz

2. **Calculate Angular Frequency (ω):**
\[ \omega = 2\pi f \]
Substituting the frequency:
\[ \omega = 2\pi \times 60 = 120\pi \, \text{rad/s} \]

3. **Calculate Inductive Reactance (X_L):**
\[ X_L = \omega L \]
Substituting the values:
\[ X_L = 120\pi \times 2 = 240\pi \, \text{ohms} \]

4. **Calculate Impedance (Z):**
The impedance in an inductive circuit is given by:
\[ Z = \sqrt{R^2 + X_L^2} \]
Substituting the values:
\[ Z = \sqrt{10^2 + (240\pi)^2} \]
Calculating \( (240\pi)^2 \):
\[ (240\pi)^2 \approx (240 \times 3.14)^2 \approx 75360 \]
Now, calculate \( Z \):
\[ Z = \sqrt{100 + 75360} \approx \sqrt{75460} \approx 274.5 \, \text{ohms} \]

5. **Calculate Current (I):**
Using Ohm's law for AC circuits:
\[ I = \frac{V}{Z} \]
Substituting the values:
\[ I = \frac{120}{274.5} \approx 0.437 \, \text{A} \]

6. **Final Result:**
The current in the circuit is approximately \( 0.44 \, \text{A} \).