A direct-current sensor heating element has an internal resistance of 12\text{ }\Omega and… — Armed Services Vocational Aptitude Battery (ASVAB)

A direct-current sensor heating element has an internal resistance of $12\text{ }\Omega$ and carries a steady current of $2.5\text{ A}$ . What is the electrical power dissipated by the heating element, in watts?

Answer: 75 W

Answer

The electrical power dissipated by the heating element is

75\text{ W}

Electrical power dissipated by a resistive element is calculated using Watt's Law as

P = I^2 R

. Squaring the current of

2.5\text{ A}

yields

6.25\text{ A}^2

, and multiplying by the resistance of

12\text{ }\Omega

results in

75\text{ W}

Step-by-Step Solution

Identify the known circuit parameters

I = 2.5\text{ A}

and

R = 12\text{ }\Omega

These are the two direct measurements provided for the resistive load.

Select the appropriate power formula

P = I^2 R

Watt's Law specifies that power dissipation through a resistance carrying a known current equals the square of the current multiplied by the resistance.

Calculate the power dissipation

P = (2.5\text{ A})^2 \times 12\text{ }\Omega = 6.25 \times 12 = 75\text{ W}

Squaring

2.5

gives

6.25

, and multiplying

6.25

12

produces

75

watts.

Key Concept

Calculating electrical power using current and resistance (

P = I^2 R

)

Estimated Time:1m 0s

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