ELECTROMAGNETISM & RELATIVITY - Chapter 3, Exercise 3 Solution
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Power Dissipated by a Heating Element

PROBLEM
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A heating element carries a current of 5 A and has a resistance of
20 ohms. Calculate the power it dissipates, using P = I^2 R.

SOLUTION
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Using the power formula:

    P = I^2 R

Substitute the given values:

    I = 5 A
    R = 20 ohms

    P = 5^2 x 20
    P = 25 x 20
    P = 500 W

ANSWER: The heating element dissipates 500 W of power.

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WHY THIS WORKS AS AN ANSWER

P = I^2 R is one of three equivalent power formulas covered in the
chapter (P = IV = I^2R = V^2/R), each useful depending on which two
quantities are already known - here, current and resistance are
given directly, so I^2R is the most direct route without needing to
first find voltage. This result also demonstrates exactly why the
device is called a "heating element" in the first place: this 500 W
of electrical power is not doing mechanical work anywhere - it is
being deliberately dissipated as heat within the resistive element
itself, the same electrical-energy-to-heat conversion the chapter's
own worked example (36 W dissipated by a resistor) demonstrates at a
smaller scale.