Question 264: AC fundamentals

Question

In an $L R$ circuit, the value of $L$ is $\left(\frac{0.3}{\pi}\right)$ henry and the value of R is $40 \Omega$, If in the circuit, 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

Accepted Answer

Step 1: Write down given data
$ L = 	frac{0.3}{\pi}\,	ext{H} $
$ R = 40 \,\Omega $
Supply voltage $ V = 230 \,	ext{V (rms)} $
Frequency $ f = 50 \,	ext{Hz} $
Step 2: Reactance of inductor
$ X_L = 2 \pi f L $
$ X_L = 2 \pi (50)\left(	frac{0.3}{\pi}ight) = 2 	imes 50 	imes 0.3 = 30 \,\Omega $
Step 3: Impedance of circuit
$ Z = \sqrt{R^2 + X_L^2} $
$ Z = \sqrt{40^2 + 30^2} = \sqrt{1600 + 900} = \sqrt{2500} = 50 \,\Omega $
Step 4: Current
$ I = \frac{V}{Z} = \frac{230}{50} = 4.6 \,	ext{A} $
Ã¢ÂÂ Final Answer:
Impedance:
$ 50 \,\Omega $
Current:
$ 4.6 \,	ext{A} $
Correct option: D

Answer

$12.5 \Omega, 9.2 \mathrm{~A}$

Answer

$46.4 \Omega, 6.4 \mathrm{~A}$

Answer

$23.2 \Omega, 5 \mathrm{~A}$

Answer

$50 \Omega, 4.6 \mathrm{~A}$

AC fundamentals

In an L R circuit, the value of L is \left(\frac{0.3}{\pi}\right) henry and the value of R is 40 \Omega, If in the circuit, 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

Choose the correct answer: