Question

what is the equivalent resistance of a circuit that contains three 10.0 ω resistors connected in parallel with a 6.0 v battery?
a. 3.33 ω
b. 0.300 ω
c. 30.0 ω
d. 60.0 ω

Explanation:

Step1: Recall the formula for resistors in parallel

For resistors \(R_1\), \(R_2\), \(R_3\) in parallel, the equivalent resistance \(R_{eq}\) is given by \(\frac{1}{R_{eq}}=\frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_3}\). Here \(R_1 = R_2=R_3 = 10.0\space\Omega\).

Step2: Substitute the values into the formula

\(\frac{1}{R_{eq}}=\frac{1}{10}+\frac{1}{10}+\frac{1}{10}=\frac{1 + 1+1}{10}=\frac{3}{10}\)

Step3: Solve for \(R_{eq}\)

Take the reciprocal of both sides: \(R_{eq}=\frac{10}{3}\approx3.33\space\Omega\)

Answer:

A. \(3.33\space\Omega\)