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 \( Z \) of the given AC series circuit with a resistance \( R \) and inductive reactance \( X_L \), we can use the following formula:

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

### Step-by-Step Solution:

1. **Identify the given values:**
- Resistance \( R = 16 \, \Omega \)
- Inductive reactance \( X_L = 12 \, \Omega \)
- Capacitive reactance \( X_C = 0 \, \Omega \) (since it is not given)

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

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

4. **Add the squares:**
\[ R^2 + X_L^2 = 256 + 144 = 400 \]

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

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

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