A series AC circuit has a resistance 8 Ω and a reactance of 6 Ω. The impedance of the circuit is :
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 10 Ω
The impedance \( Z \) is the total opposition of a series AC circuit to the current. The voltage across the resistance is in phase with the current, while the voltage across the reactance is \( 90^\circ \) out of phase, so the two oppositions add as perpendicular phasors, not as plain numbers.
\( \displaystyle Z = \sqrt{R^{2} + X^{2}} \)
\( R = 8\,\Omega \)
\( X = 6\,\Omega \)
\( \displaystyle Z = \sqrt{8^{2} + 6^{2}}\,\Omega = \sqrt{64 + 36}\,\Omega = \sqrt{100}\,\Omega = 10\,\Omega \)