A direct-current (DC) communication antenna heater operates from a 48\text{ V} power sourc… — Armed Services Vocational Aptitude Battery (ASVAB)

A direct-current (DC) communication antenna heater operates from a $48\text{ V}$ power source and dissipates $96\text{ W}$ of electrical power. What is the electrical resistance of the heater in ohms ( $\Omega$ )?

Answer: 24 Ω

Answer

The electrical resistance of the antenna heater is

24\ \Omega

According to Watt's Law, power is related to voltage and resistance by

P = \frac{V^2}{R}

. Rearranging this formula to solve for resistance gives

R = \frac{V^2}{P}

. Substituting

48\text{ V}

for voltage and

96\text{ W}

for power yields

R = \frac{48^2}{96} = \frac{2304}{96} = 24\ \Omega

Step-by-Step Solution

Select the appropriate form of Watt's Law connecting power (

P

), voltage (

V

), and resistance (

R

P = \frac{V^2}{R}

The circuit parameters given are voltage and power, with resistance as the unknown variable.

Rearrange the formula to isolate resistance (

R

R = \frac{V^2}{P}

Algebraic isolation of

R

allows direct calculation from the known values.

Substitute

V = 48\text{ V}

and

P = 96\text{ W}

into the rearranged formula and compute the result.

R = \frac{48^2}{96} = \frac{2304}{96} = 24\ \Omega

Simplifying the arithmetic yields the exact resistance value.

Key Concept

Watt's Law relates power, voltage, and resistance through the formula

P = \frac{V^2}{R}

, which rearranges to

R = \frac{V^2}{P}

Alternative Method

First find the current drawn by the heater using

I = \frac{P}{V} = \frac{96\text{ W}}{48\text{ V}} = 2\text{ A}

. Then apply Ohm's Law to determine the resistance:

R = \frac{V}{I} = \frac{48\text{ V}}{2\text{ A}} = 24\ \Omega

Estimated Time:1m 0s

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Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Alternative Method

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