Question

what is the equivalent resistance of the circuit?
a. 60.0 ω
b. 120.0 ω
c. 5.45 ω
d. 0.183 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, \(R_1 = 10.0\space\Omega\), \(R_2=20.0\space\Omega\), \(R_3 = 30.0\space\Omega\)
So, \(\frac{1}{R_{eq}}=\frac{1}{10.0}+\frac{1}{20.0}+\frac{1}{30.0}\)

Step2: Calculate the sum of the reciprocals

Find a common denominator. The common denominator of \(10\), \(20\) and \(30\) is \(60\)
\(\frac{1}{10.0}+\frac{1}{20.0}+\frac{1}{30.0}=\frac{6 + 3+ 2}{60}=\frac{11}{60}\)
So, \(\frac{1}{R_{eq}}=\frac{11}{60}\)

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

Take the reciprocal of both sides: \(R_{eq}=\frac{60}{11}\approx5.45\space\Omega\)

Answer:

C. \(5.45\space\Omega\)