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

Given:

• Resistance (R) = 4 Ω
• Inductive reactance (X_L) = 3 Ω

The impedance (Z) of an RL series circuit is calculated by: 

Z = √(R² + X_L²)

Substituting the values:

Z = √(4² + 3²) = √(16 + 9) = √25 = 5 Ω

The impedance of the circuit is 5 Ω.

Answer 2

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.