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 find the total current drawn from the battery, when two resistors are connected in parallel, we first need to calculate the equivalent resistance of the parallel combination of resistors.

For resistors in parallel, the equivalent resistance \( R_{\text{eq}} \) is given by the formula:

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

Substituting the given resistor values, \( R_1 = 4 \Omega \) and \( R_2 = 6 \Omega \):

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

To add these fractions, we find a common denominator, which is 12:

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

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

Thus:

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

Now, using Ohm's law, the total current \( I \) drawn from the battery is given by:

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

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

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

Therefore, the total current drawn from the battery is 5 A.

Answer 2

Step 1: Calculate equivalent resistance for resistors in parallel \[ \frac{1}{R_{\text{eq}}} = \frac{1}{4} + \frac{1}{6} = \frac{3}{12} + \frac{2}{12} = \frac{5}{12} \] \[ R_{\text{eq}} = \frac{12}{5} = 2.4\, \Omega \] Step 2: Use Ohm's law to find total current \[ I = \frac{V}{R_{\text{eq}}} = \frac{12}{2.4} = 5\, A \]