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Question: In the circuit shown below, the ac source has voltage \(V = 20\cos(\omega t)\) volts with \(\omega\)...

In the circuit shown below, the ac source has voltage V=20cos⁡(ωt)V = 20\cos(\omega t) volts with ω\omega = 2000 rad/sec. the amplitude of the current will be nearest to

A

2A2A

B

3.3A3.3A

C

2/5A2/\sqrt{5}A

D

5A\sqrt{5}A

Answer

2A2A

Explanation

Solution

R=6+4=10ΩR = 6 + 4 = 10\Omega

XL=ωL=2000×5×10−3=10ΩX_{L} = \omega L = 2000 \times 5 \times 10^{- 3} = 10\Omega

XC=1ωC=12000×50×10−6=10Ω∴Z=R2+(XL−XC)2=10ΩX_{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 =i0=V0Z=2010=2A= i_{0} = \frac{V_{0}}{Z} = \frac{20}{10} = 2A