A choke coil having a resistance of `10Omega` and inductance of 0.5 H is connected in series with a capacitor of 2.5 `muF`. The whole circuit has been connected to 230 V, 50 Hz supply. Calculate the value of current flowing through the circuit.

Options

A. 0.487 A
B. 0.308 A
C. 0.206 A
D. None of these

Explanation

To calculate the current flowing through the circuit, we need to follow these steps:

### Step 1: Calculate the Capacitive Reactance (Xc)
The capacitive reactance (Xc) can be calculated using the formula:
\[ X_c = \frac{1}{\omega C} \]
where:
- \(\omega = 2\pi f\) (angular frequency),
- \(f = 50 \, \text{Hz}\),
- \(C = 2.5 \, \mu F = 2.5 \times 10^{-6} \, F\).

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

Now, substitute the values into the formula for \(X_c\):
\[ X_c = \frac{1}{314.16 \times 2.5 \times 10^{-6}} \approx 1273.88 \, \Omega \]

### Step 2: Calculate the Inductive Reactance (Xl)
The inductive reactance (Xl) can be calculated using the formula:
\[ X_l = \omega L \]
where:
- \(L = 0.5 \, H\).

Substituting the values:
\[ X_l = 314.16 \times 0.5 \approx 157.08 \, \Omega \]

### Step 3: Calculate the Impedance (Z)
The total impedance (Z) in a series circuit with resistance (R), inductive reactance (Xl), and capacitive reactance (Xc) is given by:
\[ Z = \sqrt{R^2 + (X_c - X_l)^2} \]
where:
- \(R = 10 \, \Omega\).

Substituting the values:
\[ Z = \sqrt{10^2 + (1273.88 - 157.08)^2} \]
Calculating \(X_c - X_l\):
\[ X_c - X_l = 1273.88 - 157.08 = 1116.80 \, \Omega \]
Now substituting back into the impedance formula:
\[ Z = \sqrt{10^2 + (1116.80)^2} = \sqrt{100 + 1247404.64} \approx \sqrt{1247504.64} \approx 1116.90 \, \Omega \]

### Step 4: Calculate the Current (I)
Using Ohm's law, the current can be calculated as:
\[ I = \frac{V}{Z} \]
where:
- \(V = 230 \, V\).

Substituting the values:
\[ I = \frac{230}{1116.90} \approx 0.205 \, A \]

### Final Answer
The value of the current flowing through the circuit is approximately:
\[ I \approx 0.205 \, A \]

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