Question

27.2 multiloop circuits three resistors are connected in parallel. if the resistors are each 3.0ω, what is the total resistance of the circuit? save for later o 27ω o 6.0ω o 9.0ω o 1.0ω submit answer

Explanation:

Step1: Recall parallel - resistance formula

The formula for the equivalent resistance $R_{eq}$ of $n$ resistors in parallel is $\frac{1}{R_{eq}}=\sum_{i = 1}^{n}\frac{1}{R_i}$. Here, $n = 3$ and $R_1=R_2=R_3 = 3.0\Omega$.

Step2: Calculate the sum of the reciprocals

$\frac{1}{R_{eq}}=\frac{1}{3.0\Omega}+\frac{1}{3.0\Omega}+\frac{1}{3.0\Omega}=\frac{1 + 1+1}{3.0\Omega}=\frac{3}{3.0\Omega}=1\Omega^{-1}$.

Step3: Solve for $R_{eq}$

Taking the reciprocal of both sides of the equation $\frac{1}{R_{eq}} = 1\Omega^{-1}$, we get $R_{eq}=1.0\Omega$.

Answer:

$1.0\Omega$