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

Answer 1

Answer: (B)

2.828 A

Answer 2

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)
$I_{ rms} = \frac{ I_0 }{ \sqrt 2} = \frac{ 4 }{ \sqrt 2} = 2 \sqrt 2 = 2.828 \, A$