Question

The impedance of a coil connected across a single-phase AC source is \( 3 + j4 \) ohms. If another capacitive load with an impedance of \( 3 - j4 \) ohms is connected in parallel with this coil, the overall impedance seen by the AC source will be

• A. 25 ohms
• B. \( \frac{6}{25} \) ohms
• C. \( \frac{25}{6} \) ohms
• D. 6 ohms

Hint:

For parallel impedance, use the formula \( \frac{1}{Z_{\text{total}}} = \frac{1}{Z_1} + \frac{1}{Z_2} \) and simplify the complex terms.

Answer 1

The Correct Option is D

Step 1: Formula for parallel impedance.
The total impedance \( Z_{\text{total}} \) for two components in parallel is given by: \[ \frac{1}{Z_{\text{total}}} = \frac{1}{Z_1} + \frac{1}{Z_2}. \]
Step 2: Substitute the given impedances.
Given that \( Z_1 = 3 + j4 \) ohms and \( Z_2 = 3 - j4 \) ohms, we substitute these into the formula: \[ \frac{1}{Z_{\text{total}}} = \frac{1}{3 + j4} + \frac{1}{3 - j4}. \] Simplifying: \[ \frac{1}{Z_{\text{total}}} = \frac{(3 - j4) + (3 + j4)}{(3 + j4)(3 - j4)} = \frac{6}{9 + 16} = \frac{6}{25}. \] Thus: \[ Z_{\text{total}} = 6 \, \text{ohms}. \]
Step 3: Conclusion.
Thus, the overall impedance is 6 ohms, corresponding to option (D).