A `220V,50Hz` Ac source is connected to an inductance of `0.2H` and a resistance of `20ohm` in series. What is the current in the current?

Options

A. `10A`
B. `5A`
C. `33.3A`
D. `3.33A`

Explanation

To find the current flowing through the circuit with a given AC source, resistance, and inductance, we can follow these steps:

### Step 1: Identify the given values
- Voltage (V) = 220 V
- Frequency (f) = 50 Hz
- Inductance (L) = 0.2 H
- Resistance (R) = 20 Ω

### Step 2: Calculate the inductive reactance (XL)
The inductive reactance (XL) can be calculated using the formula:
\[ X_L = \omega L \]
where \( \omega = 2\pi f \).

First, calculate \( \omega \):
\[ \omega = 2\pi \times 50 = 100\pi \, \text{rad/s} \approx 314.16 \, \text{rad/s} \]

Now, calculate \( X_L \):
\[ X_L = 100\pi \times 0.2 \approx 62.83 \, \Omega \]

### Step 3: Calculate the impedance (Z)
The impedance (Z) in a series RL circuit is given by:
\[ Z = \sqrt{R^2 + X_L^2} \]

Substituting the values:
\[ Z = \sqrt{(20)^2 + (62.83)^2} \]
\[ Z = \sqrt{400 + 3945.44} \approx \sqrt{4345.44} \approx 66 \, \Omega \]

### 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:
\[ I = \frac{220}{66} \approx 3.33 \, \text{A} \]

### Final Answer
The current flowing through the circuit is approximately **3.33 A**.

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