The instantaneous voltage through a device of impedance 20 $\Omega$ is e = 80 \,sin \,100 $ \pi t$. The effective value of the current is
- 3 A
- 2.828 A
- 1.732 A
- 4 A
The Correct Option is B
Solution and Explanation
e = 80 sin 100 $ \pi t$
Comparing the given instantaneous voltage with standard instantaneous voltage
e = $ e_0 \sin \: \omega t $
we get $ e_0 = 80 \, V $
where $ e_0$ is the peak value of voltage.
Impedance (Z) = $20 \Omega$
Peak value of current $ I_0 = \frac{ e_0 }{ Z} $
= $ \frac{ 80}{ 20 } = 4 \,A $
Effective value of current (root mean square value of current)
$ I_{ rms} = \frac{ I_0 }{ \sqrt 2} = \frac{ 4 }{ \sqrt 2} = 2 \sqrt 2 = 2.828 \, A $
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Concepts Used:
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When voltage changes its direction after every half cycle is known as alternating voltage. The current flows in the circuit at that time are known as alternating current. The alternating current(AC) follows the sine function which changes its polarity concerning time. Most of the electrical devices are operating on the ac voltage.
