Parallel Circuit Physics Example 3

Follow the full solution, then compare it with the other examples linked below.

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10 \text{ } \Omega

and a

15 \text{ } \Omega

resistor are in parallel. What is the combined resistance?

1
Use the parallel formula: $\frac{1}{R_T} = \frac{1}{10} + \frac{1}{15} = \frac{3}{30} + \frac{2}{30} = \frac{5}{30}$
2
$R_T = \frac{30}{5} = 6 \text{ } \Omega$

Answer

R_T = 6 \text{ } \Omega

The parallel combination is always less than the smallest resistor. The product-over-sum shortcut also works:

R_T = \frac{10 \times 15}{10 + 15} = \frac{150}{25} = 6 \text{ } \Omega

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