Question

The motor of an electric drill draws a $3.5A$rms current at the power-line voltage of $120V$rms. What is the motor's power if the current lags the voltage by$20°$.

Short answer

The motor's power is$394.98W$.

Step-by-step solution

Given Information

We have given that $I_{rms}=3.5A$and $V_{rms}=120V$and the phase angle $\varphi =20°$.

We have to find the power of motor.

Formula Used

Now, using the formula

$P=I_{rms}.V_{rms}.\cos \varphi$let this be equation 1

where P is the power of motor and $I_{rms}$is rms current and $V_{rms}$is rms voltage and $\varphi$is the phase angle.

Simplify

Now, by putting all the values in equation 1,

We get,

$P=3.5\times 120\times \cos 20°$

On solving,

We get $P=394.98W$

Hence, the power of motor is$394.98W$