Q: Let there be n resistors R_{1}……..R_{n} with R_{max} = max(R1…….R2) and R_{min} = min {R1….Rn}. show that when are connected in parallel, the resultant resistance R_{p} < R_{min} and when they are connected in series, the resultant resistance Rs > R_{max}. Interpret the result physically.

Sol: When n resistors are connected in parallel , the equivalent resistance is :

$\displaystyle \frac{1}{R_p} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3} ….+ \frac{1}{R_n}$

$\displaystyle \frac{R_{min}}{R_p} = \frac{R_{min}}{R_1} + \frac{R_{min}}{R_2} + \frac{R_{min}}{R_3} ….+ \frac{R_{min}}{R_n} > 1$

$\displaystyle \frac{R_{min}}{R_p} > 1 $

$\displaystyle R_p < R_{min} $