A direct-current marine radio circuit contains two resistors connected in parallel: a 10\ … — Armed Services Vocational Aptitude Battery (ASVAB)

A direct-current marine radio circuit contains two resistors connected in parallel: a $10\ \Omega$ resistor and a $40\ \Omega$ resistor. What is the total equivalent resistance of this parallel circuit, in ohms?

Answer: 8 Ω

Answer

8 Ω

For two resistors in parallel with values of

10\ \Omega

and

40\ \Omega

, the total equivalent resistance is calculated using the product-over-sum formula:

R_{eq} = \frac{R_1 \times R_2}{R_1 + R_2} = \frac{10 \times 40}{10 + 40} = \frac{400}{50} = 8\ \Omega

. In any parallel circuit, the total equivalent resistance is always smaller than the smallest branch resistor.

Step-by-Step Solution

Select the appropriate formula for calculating the equivalent resistance of two parallel resistors.

R_eq = (R_1 * R_2) / (R_1 + R_2) or 1/R_eq = 1/R_1 + 1/R_2

In parallel circuits, total resistance is found by taking the reciprocal of the sum of the reciprocals, which simplifies to the product-over-sum rule for two branches.

Substitute the given resistor values (10 Ω and 40 Ω) into the product-over-sum formula.

R_eq = (10 * 40) / (10 + 40) = 400 / 50

Multiplying the branch values gives the numerator, and adding them gives the denominator.

Divide the numerator by the denominator to find the equivalent resistance.

R_eq = 8 Ω

400 divided by 50 equals 8, which is less than the smallest branch resistance (10 Ω), confirming the validity of the parallel calculation.

Key Concept

Parallel Circuit Equivalent Resistance

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