Question

Three resistors in parallel have an equivalent resistance of 5.0 Ω . Two of the resistors have resistances of 10 Ω and 30 Ω . What is the resistance of the third resistor? R= ___? express the correct units

Answer 1

The equivalent resistance for a parallel configuration is given by

$\frac{1}{R_e}\;=\;\frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_3}$ ......from here

$\frac{1}{R_3}\;=\;\frac{1}{R_e}-\frac{1}{R_1}-\frac{1}{R_2}$

$\frac{1}{R_3}\;=\;\frac{1}{5.0\;\Omega}-\frac{1}{10\;\Omega}-\frac{1}{30\;\Omega}$

$\frac{1}{R_3}\;=\;\frac{1}{15\;\Omega}$

$R_3\;=\;15\;\Omega$