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 find the current in the L-R circuit when a 120 V, 60 Hz AC voltage is applied, we will follow these steps:

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

### Step 2: Calculate the inductive reactance (X_L)
The inductive reactance (X_L) can be calculated using the formula:
\[ X_L = 2 \pi f L \]
Substituting the values:
\[ X_L = 2 \pi (60) (2) = 240 \pi \approx 753.98 \, \Omega \]

### Step 3: Calculate the impedance (Z)
The impedance (Z) of the circuit can be calculated using the formula:
\[ Z = \sqrt{R^2 + X_L^2} \]
Substituting the values:
\[ Z = \sqrt{(10)^2 + (240 \pi)^2} \]
Calculating:
\[ Z = \sqrt{100 + (753.98)^2} = \sqrt{100 + 567,610.56} \approx \sqrt{567,710.56} \approx 754.04 \, \Omega \]

### Step 4: Calculate the current (I)
Using Ohm's law for AC circuits, the current (I) can be calculated as:
\[ I = \frac{V}{Z} \]
Substituting the values:
\[ I = \frac{120}{754.04} \approx 0.159 \, A \approx 1.6 \, A \]

### Final Answer
The current in the circuit is approximately **1.6 A**.

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