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 $e_0=80V$
where $e_0$ is the peak value of voltage.
Impedance (Z) = $20\Omega$
Peak value of current $I_0=\frac{e_0}{Z}$
= $\frac{80}{20}=4A$
Effective value of current (root mean square value of current)
$I_{rms}=\frac{I_0}{\sqrt{2}}=\frac{4}{\sqrt{2}}=2\sqrt{2}=2.828A$