Let there be n resistors R 1 ............R n with R max = max (R 1 ......... R n ) and R min = min {R 1 ..... R n }. Show that when they are connected in parallel, the resultant resistance R P R max . Interpret the result physically.

Question

Let there be n resistors R 1 ............R n with R max = max (R 1 ......... R n ) and R min = min {R 1 ..... R n }. Show that when they are connected in parallel, the resultant resistance R P < R min and when they are connected in series, the resultant resistance R S > R max . Interpret the result physically.

Philoid · Accepted Answer

When the resistors are connected in parallel,

This implies,

Hence,

When the resistors are connected in series,

R_S = R₁ + R₂ + … + R_n > R_max

Comparing the figures given below,

In the first case potential across R_min is same as in case2. Hence current flowing through R_min is the same. This means total current in case2 is more than that in case1. This means for constant value of V for a greater value of I ,R_p < R_min.

Similarly,

Potential drop across R_max is less in case1 than case2. This means Current flowing through R_max in case1 is more than that in case2. Hence, for this to be possible R_s>R_max.

Let there be n resistors R1 ............Rn with Rmax = max (R1......... Rn) and Rmin = min {R1 ..... Rn}. Show that when they 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.