Question

If \( n \) equal resistors are first connected in series and then in parallel, the ratio of maximum to minimum resistance will be:

• A. \( n \)
• B. \( \frac{n}{1} \)
• C. \( x n \)
• D. \( n^2 \)

Hint:

Series resistance adds; parallel resistance divides: \[ R_{\text{series}} = nR, \quad R_{\text{parallel}} = \frac{R}{n}. \] Ratio of max to min = \( n^2 \).

Answer 1

The Correct Option is A

- When \( n \) equal resistors each of resistance \( R \) are connected in series, total resistance is: \[ R_{\text{series}} = nR, \] which is the maximum resistance. - When connected in parallel, total resistance is: \[ R_{\text{parallel}} = \frac{R}{n}, \] which is the minimum resistance. Therefore, the ratio is: \[ \frac{R_{\text{max}}}{R_{\text{min}}} = \frac{nR}{\frac{R}{n}} = n^2. \] Note: The ratio is \( n^2 \), so correct answer should be (D).