If a `16Omega`resistance and `12 Omega` inductive reactance are present in an a.c series circuit. Then the impedance of the circuit will be

Options

A. `28Omega`
B. `5 Omega`
C. `20 Omega`
D. `14sqrt2 Omega`

Answer

To find the impedance of an AC series circuit with a given resistance and inductive reactance, we can use the formula for impedance \( Z \):

\[ Z = \sqrt{R^2 + X_L^2} \]

where:
- \( R \) is the resistance,
- \( X_L \) is the inductive reactance.

### Step-by-step Solution:

1. **Identify the values**:
- Given resistance \( R = 16 \, \Omega \)
- Given inductive reactance \( X_L = 12 \, \Omega \)

2. **Substitute the values into the impedance formula**:
\[ Z = \sqrt{(16)^2 + (12)^2} \]

3. **Calculate \( R^2 \) and \( X_L^2 \)**:
- Calculate \( R^2 \):
\[ R^2 = 16^2 = 256 \]
- Calculate \( X_L^2 \):
\[ X_L^2 = 12^2 = 144 \]

4. **Add \( R^2 \) and \( X_L^2 \)**:
\[ R^2 + X_L^2 = 256 + 144 = 400 \]

5. **Take the square root to find the impedance**:
\[ Z = \sqrt{400} = 20 \, \Omega \]

### Final Answer:
The impedance of the circuit is \( 20 \, \Omega \).

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