Question

What is the rins current flowing in a \(4.50-\mathrm{kW}\) motor connected to a \(220-\mathrm{V}\) rms line when (a) the power factor is 1.00 and (b) when it is \(0.80 ?\)

Short answer

Answer: The rms currents flowing in the motor are approximately 20.45 A at a power factor of 1.00 and approximately 25.57 A at a power factor of 0.80.

Step-by-step solution

Write down the given information and the formula for power

We are given the following information: - Power of the motor: P = 4.50 kW - Voltage of the power source: V = 220 V - Two power factors: (a) pf = 1.00, (b) pf = 0.80 We will use the formula for power: \(P = V \times I \times pf\)

Convert the power to watts

Since the given power is in kW, we need to convert it to watts: Power in watts, P = 4.50 kW * 1000 = 4500 W

Calculate the rms current for power factor 1.00

Using the formula for power, we can rearrange to solve for the current I: \( I = \frac{P}{V \times pf} \) For the power factor pf = 1.00, calculate I: \( I = \frac{4500}{220 \times 1.00} \approx 20.45 A\)

Calculate the rms current for power factor 0.80

For the power factor pf = 0.80, calculate I: \( I = \frac{4500}{220 \times 0.80} \approx 25.57 A\)

Summarize the results

So, the rms current flowing in the 4.50-kW motor connected to a 220-V rms line: (a) when the power factor is 1.00, the rms current is approximately 20.45 A (b) when the power factor is 0.80, the rms current is approximately 25.57 A