An AC circuit consists of a resistance and a choke coil in series . The resistance is of 220 `Omega` and choke coils is of 0.7 H . The power abosorbed from 220 V and 50 Hz , source connected with the circuit , is

Answer

To solve the problem step by step, we need to calculate the power absorbed in an AC circuit consisting of a resistance and a choke coil in series.

### Step 1: Identify Given Values
- Resistance (R) = 220 Ω
- Inductance (L) = 0.7 H
- Voltage (V_rms) = 220 V
- Frequency (f) = 50 Hz

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

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

Now calculate \( X_L \):
\[ X_L = 100\pi \times 0.7 \approx 100 \times 3.14 \times 0.7 \approx 219.8 \, \Omega \]

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

Substituting the values:
\[ Z = \sqrt{(220)^2 + (219.8)^2} \]
Calculating \( R^2 \) and \( X_L^2 \):
\[ R^2 = 48400, \quad X_L^2 \approx 48320.04 \]
Now calculate Z:
\[ Z = \sqrt{48400 + 48320.04} \approx \sqrt{96720.04} \approx 310.9 \, \Omega \]

### Step 4: Calculate the RMS Current (I_rms)
Using Ohm's law for AC circuits:
\[ I_{rms} = \frac{V_{rms}}{Z} \]
Substituting the values:
\[ I_{rms} = \frac{220}{310.9} \approx 0.707 \, \text{A} \]

### Step 5: Calculate the Power Absorbed (P)
The power absorbed in the circuit can be calculated using:
\[ P = I_{rms}^2 \cdot R \]
Substituting the values:
\[ P = (0.707)^2 \cdot 220 \]
Calculating \( (0.707)^2 \):
\[ (0.707)^2 \approx 0.5 \]
Now calculate P:
\[ P \approx 0.5 \cdot 220 = 110 \, \text{W} \]

### Final Answer
The power absorbed from the circuit is approximately **110 Watts**.

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