An auxiliary automotive circuit connects a 12\ \text{V} direct current (DC) power source i… — Armed Services Vocational Aptitude Battery (ASVAB)

An auxiliary automotive circuit connects a $12\ \text{V}$ direct current (DC) power source in series with two resistors valued at $2\ \Omega$ and $4\ \Omega$ . What is the total current flowing through the circuit?

$2\ \text{A}$ Answer
B
$9\ \text{A}$
C
$0.5\ \text{A}$
D
$72\ \text{A}$

Answer

The total current flowing through the circuit is

2\ \text{A}

In a series circuit, total resistance is the direct sum of the individual resistors:

R_T = 2\ \Omega + 4\ \Omega = 6\ \Omega

. Using Ohm's law (

I = V / R_T

), dividing the source voltage of

12\ \text{V}

by the total resistance of

6\ \Omega

yields a total current of

2\ \text{A}

Step-by-Step Solution

Calculate the total equivalent resistance (

R_T

) of the series circuit.

R_T = R_1 + R_2 = 2\ \Omega + 4\ \Omega = 6\ \Omega

In a series circuit, total resistance equals the sum of all individual resistances.

Calculate the total circuit current (

I

) using Ohm's law.

I = \frac{V_T}{R_T} = \frac{12\ \text{V}}{6\ \Omega} = 2\ \text{A}

Ohm's law states that current equals voltage divided by total resistance.

Key Concept

Series Circuit Resistance and Ohm's Law

Estimated Time:45s

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