Question

A television set draws an rms current of \(2.50 \mathrm{A}\) from a \(60-\mathrm{Hz}\) power line. Find (a) the average current, (b) the average of the square of the current, and (c) the amplitude of the current.

Short answer

Answer: The average current is 0 A, the average of the square of the current is 6.25 A², and the amplitude of the current is 3.54 A.

Step-by-step solution

Calculate the average current

The average current for a sinusoidal waveform is actually zero. This is because there are equal times where the current is positive and negative, which ultimately cancels each other out. So, the average current is 0 A.

Calculate the average of the square of the current

To find the average of the square of the current, we square the RMS value: $$(I_{rms})^2 = (2.50 \mathrm{A})^2 = 6.25 \mathrm{A^2}$$ So, the average of the square of the current is \(6.25 \mathrm{A^2}\).

Calculate the amplitude of the current

To find the amplitude of the current, we use the formula for RMS value of a sinusoidal waveform, given by: $$I_{rms} = \frac{I_{max}}{\sqrt{2}}$$ Where \(I_{max}\) is the amplitude of the current, and \(I_{rms}\) is the RMS value. We rearrange the equation to solve for \(I_{max}\): $$I_{max} = I_{rms} \cdot \sqrt{2} = 2.50 \mathrm{A} \cdot \sqrt{2} = 3.54 \mathrm{A}$$ So, the amplitude of the current is \(3.54 \mathrm{A}\).