Five \(2 \Omega\) resistors were connected in two ways, in series and parallel. What is the ratio of the series equivalent resistance to parallel equivalent resistance?
A. \(1: 50\) B. \(2: 5\) C. 1:25 D. \(5: 6\)
Correct Answer:
Explanation
o Option is correct for the series connection \(R_{e q}=5 \times 2=10 \Omega\) for the parallel connection, \(\frac{1}{R_{\text {eq }}}=5 \times \frac{1}{2}\) $$ \frac{1}{R_{e q}}=\frac{5}{2}, R_{e q}=\frac{2}{5} \Omega $$ we are required to find \(R_{\text {oy }}\) (series) : \begin{aligned} &R_{\text {eq }} \text { (parallel). } \Rightarrow \frac{R_{\text {eq(series) }}}{R_{\text {eq(purallel })}}=\frac{10}{2 / 5} \\ &=\frac{10 \times 5}{2}=\frac{50}{2}=\frac{25}{1} \\ &\left.\therefore R_{e q}(\text { series }): \text { Req(parallel }\right) \end{aligned} \(=25: 1\)
