question_answer

What is the effective resistance of the four resistors in the circuit shown below?

A) \[\text{1}.\text{5}\,\Omega \]    

B) \[8.0\,\Omega \]                            

C) \[8.2\,\Omega \]                            

D) \[33\,\Omega \]

Correct Answer: B

Solution :

The \[3\Omega \] resistor and the\[6\Omega \]resistor are connected in parallel (have the same starting point and the same ending point). \[\frac{1}{R}=\frac{1}{3}+\frac{1}{6},\frac{1}{R}=\frac{1}{2},R=2\Omega \] The two \[12\Omega \]. resistors are connected in parallel (have the same starting point and the same ending point). \[\frac{1}{R}=\frac{1}{12}+\frac{1}{12},\frac{1}{R}=\frac{1}{6},R=6\Omega \] The \[2\Omega \] resistor (combined) and the \[6\Omega \] resistor (combined) are connected in series. Their effective resistance is \[2\Omega +6\Omega =8\Omega \] as shown below.