Four identical 40\ \Omega heating elements are connected in parallel across a 120\text{ V}… — Armed Services Vocational Aptitude Battery (ASVAB)

Four identical $40\ \Omega$ heating elements are connected in parallel across a $120\text{ V}$ power line. What is the total equivalent resistance of this circuit?

A
$160\ \Omega$
$10\ \Omega$ Answer
C
$40\ \Omega$
D
$20\ \Omega$

Answer

The total equivalent resistance of the circuit is

10\ \Omega

For

N

identical resistors of equal resistance

R

connected in parallel, the total equivalent resistance is simply the resistance of one branch divided by the total number of branches:

R_{\text{eq}} = \frac{R}{N} = \frac{40\ \Omega}{4} = 10\ \Omega

Step-by-Step Solution

Identify the number of parallel branches (

N

) and individual branch resistance (

R

N = 4

identical branches, each with

R = 40\ \Omega

Recognizing identical parallel branches allows the use of the equal-resistor shortcut formula.

Apply the parallel equivalent resistance formula for identical resistors:

R_{\text{eq}} = \frac{R}{N}

R_{\text{eq}} = \frac{40\ \Omega}{4} = 10\ \Omega

Connecting resistors in parallel creates multiple paths for electron flow, reducing the total circuit resistance below that of any individual branch.

Key Concept

Total Equivalent Resistance of Equal Parallel Resistors

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