An L-R circuit has R = 10 `Omega` and L = 2H . If 120 V , 60 Hz AC voltage is applied, then current in the circuit will be

Options

A. 0.32 A
B. 0.16 A
C. 0.45 A
D. 0.80 A

Explanation

To solve the problem of finding the current in an L-R circuit with given values, we can follow these steps:

### Step 1: Identify the given values
- Resistance, \( R = 10 \, \Omega \)
- Inductance, \( L = 2 \, H \)
- AC Voltage, \( V = 120 \, V \)
- Frequency, \( f = 60 \, Hz \)

### Step 2: Calculate the inductive reactance \( X_L \)
Inductive reactance is given by the formula:
\[ X_L = 2 \pi f L \]
Substituting the known values:
\[ X_L = 2 \pi (60) (2) = 240 \pi \, \Omega \]

### Step 3: Calculate the impedance \( Z \)
The impedance in an L-R circuit is calculated using the formula:
\[ Z = \sqrt{R^2 + X_L^2} \]
Substituting the values of \( R \) and \( X_L \):
\[ Z = \sqrt{10^2 + (240 \pi)^2} \]
Calculating \( (240 \pi)^2 \):
\[ (240 \pi)^2 \approx (240 \times 3.14)^2 \approx (753.6)^2 \approx 567,200 \]
Now substituting back into the impedance formula:
\[ Z = \sqrt{100 + 567200} = \sqrt{567300} \approx 754.8 \, \Omega \]

### Step 4: Calculate the current \( I \)
Using Ohm's law for AC circuits, the current can be calculated as:
\[ I = \frac{V}{Z} \]
Substituting the values:
\[ I = \frac{120}{754.8} \approx 0.159 \, A \]

### Conclusion
The current in the circuit is approximately \( 0.16 \, A \).