Question

An a.c. circuit contains a 4 Ω resistance wire in series with an inductance coil of reactance 3 Ω. The impedance of the circuit is:

• A. 5 Ω
• B. $∞$
• C. 34​ Ω
• D. 43​ Ω

Answer 1

The Correct Option is A

In an AC circuit containing resistance and inductance in series, the impedance Z is the vector sum of the resistance R and the inductive reactance XL​. The formula for impedance in such a circuit is
\(Z = \sqrt{R^2 + X_L^2}\)
Here, R=4Ω (resistance), and XL​=3Ω (inductive reactance).
Using the formula, we get
\(Z = \sqrt{4^2 + 3^2} = \sqrt{16 + 9} = \sqrt{25} = 5 \, \Omega\)
Thus, the total impedance of the circuit is 5Ω.