A direct current circuit contains two resistors connected in parallel across a power sourc… — Armed Services Vocational Aptitude Battery (ASVAB)

A direct current circuit contains two resistors connected in parallel across a power source. The first resistor has a resistance of $30\ \Omega$ and the second resistor has a resistance of $60\ \Omega$ . What is the total equivalent resistance of the circuit in ohms ( $\Omega$ )?

Answer: 20 ohms

Answer

The total equivalent resistance of the circuit is

20\ \Omega

For two resistors in parallel, total equivalent resistance is determined by

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

. Substituting

30\ \Omega

and

60\ \Omega

yields

\frac{1800}{90} = 20\ \Omega

Step-by-Step Solution

Select the appropriate equivalent resistance formula for parallel branches.

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

When two resistors are connected in parallel, the product-over-sum formula directly provides the total equivalent resistance.

Substitute the resistor values into the formula and solve.

R_{eq} = \frac{30 \times 60}{30 + 60} = \frac{1800}{90} = 20\ \Omega

Evaluate the arithmetic expression to calculate the equivalent circuit resistance.

Key Concept

Total equivalent resistance of parallel resistors

Alternative Method

Using the standard reciprocal formula:

\frac{1}{R_{eq}} = \frac{1}{30} + \frac{1}{60} = \frac{2}{60} + \frac{1}{60} = \frac{3}{60} = \frac{1}{20}

. Inverting both sides gives

R_{eq} = 20\ \Omega

Estimated Time:45s

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