Question

find the total resistance of the parallel circuit
R1= 5.0
R2= 10.0
R3= 20.0

Answer 1

To find the total resistance \( R_t \) in a parallel circuit, you can use the following formula:

\[
\frac{1}{R_t} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3}
\]

Given:
- \( R_1 = 5.0 \, \Omega \)
- \( R_2 = 10.0 \, \Omega \)
- \( R_3 = 20.0 \, \Omega \)

Substituting the values into the formula:

\[
\frac{1}{R_t} = \frac{1}{5.0} + \frac{1}{10.0} + \frac{1}{20.0}
\]

Calculating each term:

\[
\frac{1}{5.0} = 0.2
\]
\[
\frac{1}{10.0} = 0.1
\]
\[
\frac{1}{20.0} = 0.05
\]

Now, summing these values:

\[
\frac{1}{R_t} = 0.2 + 0.1 + 0.05 = 0.35
\]

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

\[
R_t = \frac{1}{0.35} \approx 2.86 \, \Omega
\]

Thus, the total resistance of the parallel circuit is approximately **2.86 ohms**.