Question

A sinusoidal voltage $V=200\sin 314t$ is appiled to a $10\Omega$ resistor. Find (i) rms voltage, (ii) rms current and (iii) power dissipated as heat.

Answer 1

According to the question $V=200\sin 314t$ and $R=10\Omega$

comaring it with original equation we get ,$V_m=200V$

(1} rms voltage , $V_{rms}=\frac{V_m}{\sqrt{2}}=0.707\times 200=141.4V$

(2)rms current , $I_{rms}=\frac{V_{rms}}{R}=\frac{141.4}{10}=14.14$A

(3)power dissipate ,$P=V_{rms}{I}_{rms}\cos \theta$

here $\cos \theta$ is power factor which is equal to 1 for pure resistive circuit since voltage and current are in same phase,

$p=141.4\times 14.14=1999.69\simeq 2000W$