Question

The instantaneous voltage through a device of impedance 20 $\Omega$ is e = 80 \,sin \,100 $ \pi t$. The effective value of the current is

• A. 3 A
• B. 2.828 A
• C. 1.732 A
• D. 4 A
• E. $ \sqrt 2 $ A

Answer 1

Answer: (B)

The instantaneous voltage through the given device
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 $