An inductive circuit contains a resistance of 10 ohms and an inductance of 2 henry. If an alternating voltage of 120 V and frequency 60 Hz is applied to this circuit, the current in the circuit would be nearly

Options

A. 0.32 A
B. 0.80 A
C. 0.48 A
D. 0.16 A

Answer

To solve the problem step by step, we will follow the outlined process to find the current in the inductive circuit when an alternating voltage is applied.

### Step 1: Identify Given Values
- Resistance (R) = 10 ohms
- Inductance (L) = 2 henries
- Voltage (V) = 120 volts
- Frequency (f) = 60 Hz

### Step 2: Calculate Angular Frequency (ω)
The angular frequency (ω) is calculated using the formula:
\[ \omega = 2\pi f \]
Substituting the given frequency:
\[ \omega = 2\pi \times 60 = 120\pi \text{ rad/s} \]

### Step 3: Calculate Inductive Reactance (XL)
Inductive reactance (XL) is given by the formula:
\[ X_L = \omega L \]
Substituting the values of ω and L:
\[ X_L = (120\pi) \times 2 = 240\pi \text{ ohms} \]

### Step 4: Calculate Impedance (Z)
The impedance (Z) in an inductive circuit is calculated using the formula:
\[ Z = \sqrt{R^2 + X_L^2} \]
Substituting the values of R and XL:
\[ Z = \sqrt{10^2 + (240\pi)^2} \]
Calculating \( (240\pi)^2 \):
\[ (240\pi)^2 \approx 180,000 \text{ (using } \pi \approx 3.14\text{)} \]
Thus,
\[ Z = \sqrt{100 + 180000} = \sqrt{180100} \approx 424.5 \text{ ohms} \]

### Step 5: Calculate Current (I)
The current (I) in the circuit can be found using Ohm's law for AC circuits:
\[ I = \frac{V}{Z} \]
Substituting the values of V and Z:
\[ I = \frac{120}{424.5} \approx 0.283 \text{ A} \]

### Step 6: Round the Current Value
Rounding the calculated current to two decimal places:
\[ I \approx 0.28 \text{ A} \]

### Final Answer
The current in the circuit would be nearly **0.28 A**.

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