Question

In an $LR$ circuit, the value of $L$ is $(0.3/\pi)$ henry and the value of $R$ is $40 \Omega$. If an alternating e.m.f of 230 V at 50 cycles per second is connected, the impedance of the circuit and current will be respectively ______.

• A. $12.5 \Omega$, 9.2 A
• B. $46.4 \Omega$, 6.4 A
• C. $23.2 \Omega$, 5 A
• D. $50 \Omega$, 4.6 A

Hint:

Recognizing the 3-4-5 Pythagorean triplet ($30\Omega, 40\Omega \rightarrow 50\Omega$) immediately saves you from doing the manual square root calculation for impedance!

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
In an AC circuit with a resistor and inductor, the total opposition to current is called impedance ($Z$), calculated as $Z = \sqrt{R^2 + X_L^2}$.

Step 2: Formula Application:
Inductive reactance $X_L = 2\pi f L = 2\pi(50)(0.3/\pi) = 100 \times 0.3 = 30 \Omega$. Impedance $Z = \sqrt{40^2 + 30^2} = \sqrt{1600 + 900} = \sqrt{2500} = 50 \Omega$.

Step 3: Explanation:
RMS Current $I = \frac{V}{Z} = \frac{230}{50} = 4.6$ A.

Step 4: Final Answer:
Impedance is $50 \Omega$ and current is 4.6 A.