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.

This parallel circuit has two resistors at 15 and 40 ohms. What is the total resistance?

Answer 1

In a parallel circuit, the total resistance \( R_t \) can be calculated using the formula:

\[
\frac{1}{R_t} = \frac{1}{R_1} + \frac{1}{R_2}
\]

where:
- \( R_1 \) is the resistance of the first resistor (15 Ohms)
- \( R_2 \) is the resistance of the second resistor (40 Ohms)

Plugging in the values:

\[
\frac{1}{R_t} = \frac{1}{15} + \frac{1}{40}
\]

First, we need to find a common denominator, which is 120:

\[
\frac{1}{15} = \frac{8}{120} \quad \text{and} \quad \frac{1}{40} = \frac{3}{120}
\]

Now, we can add the fractions:

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

Now, take the reciprocal to find \( R_t \):

\[
R_t = \frac{120}{11} \approx 10.909 \text{ Ohms}
\]

Rounding to one decimal place:

\[
R_t \approx 10.9 \text{ Ohms}
\]

So, the total resistance of the circuit is approximately **10.9 Ohms**.