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GUJCET · Physics · Current Electricity
You are given n resistors each of resistance r. They are first connected to get the minimum possible resistance. In the second case, they are again connected differently to get the maximum possible resistance. Calculate the ratio between minimum and maximum values of resistance so obtained.
- A \(n^2\)
- B \(\frac{1}{n^2}\)
- C \(\frac{1}{n}\)
- D n
Answer & Solution
Correct Answer
(B) \(\frac{1}{n^2}\)
Step-by-step Solution
Detailed explanation
(B)
n resistance are connected in parallel to get minimum resistance \(r_{\text {min }}=\frac{r}{n}\) Now they are connected in series to get maximum resistance
\(r_{\text {max }}=n r\)\(\frac{R_{\min }}{R_{\max }}=\frac{r}{n \times n r}=\frac{1}{n^2}\)
n resistance are connected in parallel to get minimum resistance \(r_{\text {min }}=\frac{r}{n}\) Now they are connected in series to get maximum resistance
\(r_{\text {max }}=n r\)\(\frac{R_{\min }}{R_{\max }}=\frac{r}{n \times n r}=\frac{1}{n^2}\)
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