Q: Let there be n resistors R1……..Rn with Rmax = max(R1…….R2) and Rmin = min {R1….Rn}. show that when are connected in parallel, the resultant resistance Rp < Rmin and when they are connected in series, the resultant resistance Rs > Rmax. 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} $