Question

An alternating voltage $V=30\sin 50t+40\cos 50t$ is applied to a resistor of resistance $10\Omega$. The rms value of current through resistor is:

• A. $\frac{5}{\sqrt{2}}A$
• B. $\frac{10}{\sqrt{2}}A$
• C. $5A$
• D. None of these

Answer 1

The correct option is A $\frac{5}{\sqrt{2}}A$

$I=\frac{V}{R}=\frac{30}{10}\sin 50t+\frac{40}{10}\cos 50t$

$I=3\sin 50t+4\cos 50t$

$I=5[\frac{4}{5}cos50t+\frac{3}{5}sin50t]$

$I=5[\cos 37\cos 50t+\sin 37\sin 50t]$

$I=5\cos [50t-37]$

Now,

$I_{rms}=\frac{I_0}{\sqrt{2}}=\frac{5}{\sqrt{2}}$