A coil has an inductance of 0.5 H is connected in series with a resistance of 50 `Omega` to 240 V, 50 Hz AC. The maximum current in the circuit is

Options

A. 2.5 A
B. 14.5A
C. 1.50A
D. 1.45A

Explanation

To find the maximum current in the given RL circuit, we can follow these steps:

### Step 1: Identify the given values
- Inductance (L) = 0.5 H
- Resistance (R) = 50 Ω
- Voltage (V) = 240 V
- Frequency (f) = 50 Hz

### Step 2: Calculate the angular frequency (ω)
The angular frequency (ω) is given by the formula:
\[ \omega = 2\pi f \]
Substituting the value of frequency:
\[ \omega = 2\pi \times 50 = 100\pi \, \text{rad/s} \]

### Step 3: Calculate the inductive reactance (X_L)
The inductive reactance (X_L) is calculated using the formula:
\[ X_L = \omega L \]
Substituting the values of ω and L:
\[ X_L = 100\pi \times 0.5 = 50\pi \approx 157.08 \, \Omega \]

### Step 4: Calculate the total impedance (Z)
The total impedance (Z) in an RL circuit is given by:
\[ Z = \sqrt{R^2 + X_L^2} \]
Substituting the values of R and X_L:
\[ Z = \sqrt{50^2 + (50\pi)^2} \]
Calculating:
\[ Z = \sqrt{2500 + (157.08)^2} \approx \sqrt{2500 + 24649.62} \approx \sqrt{27149.62} \approx 164.77 \, \Omega \]

### Step 5: Calculate the maximum current (I_max)
The maximum current (I_max) in the circuit can be calculated using Ohm's law:
\[ I_{\text{max}} = \frac{V}{Z} \]
Substituting the values of V and Z:
\[ I_{\text{max}} = \frac{240}{164.77} \approx 1.45 \, \text{A} \]

### Final Answer
The maximum current in the circuit is approximately **1.45 A**.

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