Electric Circuits and Resistance: Question 10

Worked solution

Step 1: Recall the relationship for resistors in parallel

$\frac{1}{R_{\text{total}}} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3}$

Step 2: Substitute the values

The resistances are $R_1 = 10\,\Omega$, $R_2 = 10\,\Omega$ and $R_3 = 5.0\,\Omega$:

$\frac{1}{R_{\text{total}}} = \frac{1}{10} + \frac{1}{10} + \frac{1}{5.0} = 0.1 + 0.1 + 0.2$

$\frac{1}{R_{\text{total}}} = 0.4$

Step 3: Take the reciprocal to find $R_{\text{total}}$

$R_{\text{total}} = \frac{1}{0.4}$

$R_{\text{total}} = \boxed{2.5\,\Omega}$

This is less than the smallest individual resistor ($R_3 = 5.0\,\Omega$), as it must be. The combined resistance of resistors in parallel is always smaller than the smallest individual resistance, since each extra branch gives the current an additional path to flow along.

Why the other options are wrong

Final answers

• Combined resistance $= \boxed{2.5\,\Omega}$, option B