Question

A sinusoidal voltage $V=200sin314t$ is applied to a $10\Omega$ resistor. Find power dissipated as heat.

• A. $500W$
• B. $1000W$
• C. $2000W$
• D. $3000W$

Answer 1

The correct option is C $2000W$

$Answer:-$ C

General sinusoidal voltage variation is given by:

$V=V_{0}sin\left(\omega t\right)$

Here, in this equation $V_0$ is peak voltage.

So, on comparing both equation we get:

$V_0=200V,\omega =314$

Relation between rms voltage and peak voltage is:

$V_{rms}=\frac{V_0}{\sqrt{2}}=\frac{200}{\sqrt{2}}=141.4V$

Relation between rms current and peak current is:

$I_{rms}=\frac{V_{rms}}{R}=\frac{141.4}{10}=14.14A$

$P=V_{rms}\times I_{rms}=141.4\times 14.14=1999.396W$