Question

the motor of an electric drill draws a 3.4 a rms current at the power-line voltage of 120 v rms. What is the motor's power if the current lags the voltage by 16??

Answer 1

The motor's power can be calculated using the formula P = IVcos(φ). Given the 3.4 A current, 120 V voltage, and a 16-degree phase lag, the motor's power is approximately 391.7 watts.

Step-by-step explanation:

Understanding Electric Motor Power

The power consumed by the motor of an electric drill can be calculated using the formula P = IVcos(φ), where P is the power in watts, I is the current in amperes, V is the voltage in volts, and φ is the phase angle between the current and voltage. The student has provided that the motor draws a 3.4 A RMS current at a power-line voltage of 120 V RMS, and the current lags the voltage by 16 degrees.

To calculate the power:

1. Use the given RMS current (I) of 3.4 A.
2. Use the given RMS voltage (V) of 120 V.
3. Calculate the cosine of the phase angle (φ), which is 16 degrees. The cosine of 16 degrees is approximately 0.961.
4. Multiply I, V, and the cosine of φ to find the power P: P = 3.4 A * 120 V * 0.961 ≈ 391.7 watts.

Therefore, the motor's power is approximately 391.7 watts when the current lags the voltage by 16 degrees.