Question

A circuit diagram with a power source labeled negative positive V and two parallel resistors 15 Ohms and 40 Ohms. There are two vectors in a clockwise direction labeled I.
Round your answers to one decimal place.

If there is a 12 V battery in the circuit, what would the approximate current be?

Answer 1

To find the total current (I) in the circuit with a 12 V battery and two resistors in parallel (15 Ohms and 40 Ohms), we first need to calculate the equivalent resistance (R_eq) of the parallel resistors.

The formula for the equivalent resistance of resistors in parallel is:

\[
\frac{1}{R_{eq}} = \frac{1}{R_1} + \frac{1}{R_2}
\]

Substituting the values of R_1 and R_2 (15 Ohms and 40 Ohms):

\[
\frac{1}{R_{eq}} = \frac{1}{15} + \frac{1}{40}
\]

To find a common denominator, we can use 120:

\[
\frac{1}{R_{eq}} = \frac{8}{120} + \frac{3}{120} = \frac{11}{120}
\]

Now taking the reciprocal to find R_eq:

\[
R_{eq} = \frac{120}{11} \approx 10.91 \, \text{Ohms}
\]

Next, we can use Ohm's Law (V = I * R) to find the total current (I) flowing through the circuit. Rearranging this gives us:

\[
I = \frac{V}{R_{eq}}
\]

Substituting in the values (V = 12 V and R_eq ≈ 10.91 Ohms):

\[
I = \frac{12 \, \text{V}}{10.91 \, \text{Ohms}} \approx 1.1 \, \text{A}
\]

Therefore, the approximate total current flowing through the circuit is **1.1 A**.