Question

Two resistors, 4 $\Omega$ and 6 $\Omega$, are connected in parallel to a 12 V battery. What is the total current drawn from the battery?

• A. 3 A
• B. 5 A
• C. 4 A
• D. 6 A

Hint:

For resistors in parallel, total resistance is found by the reciprocal formula and total current by Ohm's law \(I = V/R\).

Answer 1

The Correct Option is B

To determine the total current supplied by the battery when two resistors are connected in parallel, first calculate the equivalent resistance of the parallel combination.

The equivalent resistance \( R_{\text{eq}} \) for parallel resistors is calculated using the formula:

\( \frac{1}{R_{\text{eq}}} = \frac{1}{R_1} + \frac{1}{R_2} \)

Given \( R_1 = 4 \Omega \) and \( R_2 = 6 \Omega \), substitute these values:

\( \frac{1}{R_{\text{eq}}} = \frac{1}{4} + \frac{1}{6} \)

Adding the fractions requires a common denominator, which is 12:

\( \frac{1}{4} = \frac{3}{12}, \quad \frac{1}{6} = \frac{2}{12} \)

\( \frac{1}{R_{\text{eq}}} = \frac{3}{12} + \frac{2}{12} = \frac{5}{12} \)

This yields:

\( R_{\text{eq}} = \frac{12}{5} \Omega = 2.4 \Omega \)

Ohm's law \( I = \frac{V}{R_{\text{eq}}} \) is then used to find the total current \( I \):

\( I = \frac{V}{R_{\text{eq}}} \)

With \( V = 12 \text{ V} \):

\( I = \frac{12 \text{ V}}{2.4 \Omega} = 5 \text{ A} \)

The total current drawn from the battery is consequently 5 A.