In a motor for a drill the current lags the voltage by 20.0°. The motor draws an rms current of 6.10 A at a voltage of 150. V rms. What is the motor's power?
Question
In a motor for a drill the current lags the voltage by 20.0°. The motor draws an rms current of 6.10 A at a voltage of 150. V rms. What is the motor's power?
Solution
The power in an AC circuit is given by the formula P = VIcos(θ), where V is the voltage, I is the current, and θ is the phase angle between the current and the voltage.
In this case, V = 150 V, I = 6.10 A, and θ = 20.0°.
First, we need to convert the phase angle from degrees to radians because the cosine function in calculators typically uses radians. We can do this using the conversion factor π radians = 180°.
So, θ = 20.0° * (π / 180) = 0.349 radians.
Now we can substitute these values into the power formula:
P = (150 V)(6.10 A)cos(0.349 radians) = 870.6 W.
So, the motor's power is approximately 870.6 Watts.
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