Electro Magnetic Induction And Alternating Currents Question 52

Question: In the circuit shown below, the ac source has voltage $ V=20\cos (\omega t) $ volts with $ \omega $ = 2000 rad/sec. the amplitude of the current will be nearest to [AMU (Engg.) 2000]

Options:

A) $ 2A $

B) $ 3.3A $

C) $ 2/\sqrt{5}A $

D) $ \sqrt{5}A $

Show Answer

Answer:

Correct Answer: A

Solution:

$ R=6+4=10,\Omega $

$ X_{L}=\omega L=2000\times 5\times {{10}^{-3}}=10,\Omega $

$ X_{C}=\frac{1}{\omega C}=\frac{1}{2000\times 50\times {{10}^{-6}}}=10,\Omega $
$ \therefore Z=\sqrt{R^{2}+{{(X_{L}-X_{C})}^{2}}}=10,\Omega $

Amplitude of current $ =i_{0}=\frac{V_{0}}{Z}=\frac{20}{10}=2A $



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