if r1 = 40.0 ω, r2 = 25.4 ω, and r3 = 70.8 ω, what is the equivalent resistance? req = ? ω

Explanation:

Step1: Calculate parallel - resistance of R1 and R3

For two resistors in parallel $R_{13}$, the formula is $\frac{1}{R_{13}}=\frac{1}{R_{1}}+\frac{1}{R_{3}}$. $\frac{1}{R_{13}}=\frac{1}{40.0}+\frac{1}{70.8}$ $=\frac{70.8 + 40.0}{40.0\times70.8}=\frac{110.8}{2832}$ $R_{13}=\frac{2832}{110.8}\approx25.56\ \Omega$

Step2: Calculate total equivalent resistance

$R_{13}$ is in series with $R_{2}$. The formula for resistors in series is $R_{eq}=R_{13}+R_{2}$. $R_{eq}=25.56 + 25.4$ $R_{eq}=50.96\ \Omega$

Answer:

$50.96$