Electro Magnetic Induction And Alternating Currents Question 147
Question: A virtual current of 4A and 50 Hz flows in an ac circuit containing a coil. The power consumed in the coil is 240 W. If the virtual voltage across the coil is 100 V its inductance will be
Options:
A) $ \frac{1}{3\pi } $ H
B) $ \frac{1}{5\pi }H $
C) $ \frac{1}{7\pi }H $
D) $ \frac{1}{9\pi }H $
Show Answer
Answer:
Correct Answer: B
Solution:
$ R=\frac{P}{i_{rms}^{2}}=\frac{240}{16}=15\Omega $
$ Z=\frac{V}{i}=\frac{100}{4}=25\Omega $
Now $ X_{L}=\sqrt{Z^{2}-R^{2}}=\sqrt{{{(25)}^{2}}-{{(15)}^{2}}}=20\Omega $
$ \therefore 2\pi \nu L=20\Rightarrow L=\frac{20}{2\pi \times 50}=\frac{1}{5\pi }Hz $
