Question 438: Current Electricity

Question

The resistance of the series combination of two resistances is $S.$ When they are jointed in parallel the total resistance is $P.$ If $S = nP$ then the Minimum possible value of $n$ is

Accepted Answer

$S = {R_1} + {R_2}$ and $P = {{{R_1}{R_2}} \over {{R_1} + {R_2}}}$
$S = nP \Rightarrow {R_1} + {R_2} = {{n\left( {{R_1}{R_2}} \right)} \over {\left( {{R_1} + {R_2}} \right)}}$
$ \Rightarrow {\left( {{R_1} + {R_2}} \right)^2} = n{R_1}{R_2}$
$ \Rightarrow n = {{R_1^1 + R_2^2 + {R_1}{R_2}} \over {{R_1}{R_2}}}$
$n = {{{R_1}} \over {{R_2}}} + {{{R_2}} \over {{R_1}}} + 2$
Arithmetic mean $ > $ Geometric mean
Minimum value of $n$ is $4$

Answer

$2$

Answer

$3$

Answer

$4$

Answer

$1$

Current Electricity

The resistance of the series combination of two resistances is S. When they are jointed in parallel the total resistance is P. If S = nP then the Minimum possible value of n is

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