An off-grid solar installation supplies direct-current (DC) power to two ventilation fan c… — Armed Services Vocational Aptitude Battery (ASVAB)

An off-grid solar installation supplies direct-current (DC) power to two ventilation fan circuits connected in parallel across the main distribution bus. The primary intake fan circuit presents a resistance of $40\ \Omega$ , while the secondary exhaust fan circuit presents a resistance of $60\ \Omega$ . What is the total equivalent resistance of these two parallel circuits combined?

A
$100\ \Omega$
$24\ \Omega$ Answer
C
$50\ \Omega$
D
$20\ \Omega$

Answer

24\ \Omega

For two resistors connected in parallel, the total equivalent resistance (

R_{\text{eq}}

) is calculated using the product-over-sum formula:

R_{\text{eq}} = \frac{R_1 \times R_2}{R_1 + R_2}

. Substituting the circuit values yields

R_{\text{eq}} = \frac{40 \times 60}{40 + 60} = \frac{2400}{100} = 24\ \Omega

. In any parallel circuit, the total equivalent resistance must always be less than the resistance of the smallest branch (

24\ \Omega < 40\ \Omega

Step-by-Step Solution

Identify the parallel resistance formula for two branch loads

R_{\text{eq}} = \frac{R_1 \times R_2}{R_1 + R_2}

The equivalent resistance of two parallel resistors is given by their product divided by their sum.

Calculate the product of the two branch resistances

40\ \Omega \times 60\ \Omega = 2400\ \Omega^2

Multiplying the individual branch values forms the numerator of the formula.

Calculate the sum of the two branch resistances

40\ \Omega + 60\ \Omega = 100\ \Omega

Adding the branch values forms the denominator of the formula.

Divide the product by the sum to determine equivalent resistance

R_{\text{eq}} = \frac{2400}{100} = 24\ \Omega

Evaluating the quotient provides the total opposition to current flow across the parallel network.

Key Concept

Parallel Equivalent Resistance

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