Question

If n equal resistances are first connected in series and then connected in parallel, the ratio of the maximum resistance to the minimum resistance is

• A. n
• B. $\frac{1}{n^2}$
  
• C. $n^2$
  
• D. $\frac{1}{n}$

Answer 1

The correct option is C

$n^2$

Let 'n' be the number of resistors, 'R' be the value of each resistor.

Equivalent resistance of the circuit when the resistors are connected in series, $R_s=nR$
Equivalent resistance of the circuit when the resistors are connected in parallel,$R_p=\frac{R}{n}$

Hence its clear that the equivalent resistance of series circuit is high compared to parallel circuit.
$\therefore \frac{R_{max}}{R_{min}}=\frac{R_s}{R_p}=\frac{nR}{\left(\frac{R}{n}\right)}=n^2$