Question

Show that for some equal resistors connected in series and then in parallel, the ratio of
equivalent resistance will be square of number of resistors:1

Answer 1

Answer:

SUPPOSE TOTAL NUMBER OF RESISTERS USED = 2

LET EACH RESISTER HAVE RESISTANCE = R

• NOW IF WE CONNECT THEM IN SERIES THEN

Req=R+R=2R

• NOW IF WE CONNECT THEM IN PARALLEL THEN

$\frac{1}{Req} = \frac{1}{R} + \frac{1}{R} = \frac{2}{R} \\ \frac{1}{Req} = \frac{2}{R} \\ Req = \frac{R}{2}$

NOW RATIO OF TWO OBTAINED RESULTS =

$= \frac{2R}{ \frac{R}{2} } = \frac{2R \times 2}{R} = 2 \times 2 = {2 }^{2} \\ \\ \\ which \: is \: equal \: to \: square \: of \: total \: number \: of \: resister \: used$