A source of 220V is applied in an A.C. circuit. The value of resistance is `220Omega`. Frequency & inductance are 50 Hz and 0.7 H, then wattless current is

Options

A. 0.5 amp
B. 0.7 amp
C. 1.0 amp
D. None

Answer

To find the wattless current in the given AC circuit, we can follow these steps:

### Step 1: Identify the given values
- Voltage (V) = 220 V
- Resistance (R) = 220 Ω
- Frequency (f) = 50 Hz
- Inductance (L) = 0.7 H

### Step 2: Calculate the maximum current (I₀)
The maximum current (I₀) can be calculated using Ohm's law:
\[ I₀ = \frac{V}{R} \]
Substituting the values:
\[ I₀ = \frac{220 \, \text{V}}{220 \, \Omega} = 1 \, \text{A} \]

### Step 3: Calculate the RMS current (Iₘₛ)
The RMS current (Iₘₛ) is given by:
\[ Iₘₛ = \frac{I₀}{\sqrt{2}} \]
Substituting the value of I₀:
\[ Iₘₛ = \frac{1 \, \text{A}}{\sqrt{2}} \approx 0.707 \, \text{A} \]

### Step 4: Calculate the inductive reactance (Xₗ)
The inductive reactance (Xₗ) can be calculated using the formula:
\[ Xₗ = 2 \pi f L \]
Substituting the values:
\[ Xₗ = 2 \pi (50 \, \text{Hz}) (0.7 \, \text{H}) \]
\[ Xₗ \approx 2 \times 3.14 \times 50 \times 0.7 \approx 220 \, \Omega \]

### Step 5: Calculate the phase angle (φ)
The phase angle (φ) can be calculated using:
\[ \tan φ = \frac{Xₗ}{R} \]
Substituting the values:
\[ \tan φ = \frac{220 \, \Omega}{220 \, \Omega} = 1 \]
Thus,
\[ φ = 45^\circ \]

### Step 6: Calculate the wattless current (Iₗ)
The wattless current (Iₗ) can be calculated using:
\[ Iₗ = Iₘₛ \sin φ \]
Since \( \sin 45^\circ = \frac{1}{\sqrt{2}} \):
\[ Iₗ = 0.707 \, \text{A} \times \frac{1}{\sqrt{2}} \]
\[ Iₗ = \frac{0.707}{\sqrt{2}} = 0.5 \, \text{A} \]

### Final Answer:
The wattless current is \( 0.5 \, \text{A} \).

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