In L-R circuit, resistance is `8Omega` and inductive reactance is `6Omega` then impedance is:

Options

A. `2Omega`
B. `14Omega`
C. `4Omega`
D. `10Omega`

Answer

To find the impedance \( Z \) in an L-R circuit where the resistance \( R \) is \( 8 \, \Omega \) and the inductive reactance \( X_L \) is \( 6 \, \Omega \), we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Resistance \( R = 8 \, \Omega \)
- Inductive Reactance \( X_L = 6 \, \Omega \)

2. **Use the Impedance Formula:**
The impedance \( Z \) in an L-R circuit is calculated using the formula:
\[ Z = \sqrt{R^2 + X_L^2} \]

3. **Substitute the Values into the Formula:**
Substitute the known values of \( R \) and \( X_L \) into the formula:
\[ Z = \sqrt{(8 \, \Omega)^2 + (6 \, \Omega)^2} \]

4. **Calculate the Squares:**
Calculate \( R^2 \) and \( X_L^2 \):
\[ R^2 = 8^2 = 64 \]
\[ X_L^2 = 6^2 = 36 \]

5. **Add the Squares:**
Now, add the results:
\[ R^2 + X_L^2 = 64 + 36 = 100 \]

6. **Take the Square Root:**
Finally, take the square root to find \( Z \):
\[ Z = \sqrt{100} = 10 \, \Omega \]

### Final Answer:
The impedance \( Z \) is \( 10 \, \Omega \).

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