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Chapter 21: Problem 3

A \(1500-\) W heater runs on \(120 \mathrm{V}\) ms. What is the peak current through the heater? (Wtorial: power in ac circuits)

Short Answer

Expert verified
Answer: The peak current through the heater is approximately 17.68 A.

Step by step solution

01

Determine the rms current

To find the rms current through the heater, use the power formula for AC circuits: $$ P = V_{rms} \cdot I_{rms} $$ Rearrange the formula to solve for rms current: $$ I_{rms} = \frac{P}{V_{rms}} $$ Substitute the given values for power and voltage: $$ I_{rms} = \frac{1500 \mathrm{W}}{120 \mathrm{V}} $$
02

Calculate the rms current

Divide the power by the voltage to find the rms current: $$ I_{rms} = \frac{1500 \mathrm{W}}{120 \mathrm{V}} = 12.5 \ \mathrm{A} $$ So, the rms current through the heater is 12.5 A.
03

Determine the peak current

Since we have the rms current, we can now find the peak current using the relationship between the rms and peak currents: $$ I_{peak} = \sqrt{2} \cdot I_{rms} $$ Substitute the given rms current value: $$ I_{peak} = \sqrt{2} \cdot 12.5 \ \mathrm{A} $$
04

Calculate the peak current

Multiply the rms current by the square root of 2 to find the peak current: $$ I_{peak} = \sqrt{2} \cdot 12.5 \ \mathrm{A} \approx 17.68 \ \mathrm{A} $$ The peak current through the heater is approximately 17.68 A.

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Most popular questions from this chapter

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