$R_1 $ અને $ R_2 $ અવરોધના શ્રેણી અને સમાંતરના સમતુલ્યનો ગુણોત્તર $n$ હોય,તો...

Question

A${\left( {\frac{{{R_1}}}{{{R_2}}}} \right)^2} + {\left( {\frac{{{R_2}}}{{{R_1}}}} \right)^2} = {n^2}$
B${\left( {\frac{{{R_1}}}{{{R_2}}}} \right)^{3/2}} + {\left( {\frac{{{R_2}}}{{{R_1}}}} \right)^{3/2}} = {n^{3/2}}$
C$\left( {\frac{{{R_1}}}{{{R_2}}}} \right) + \left( {\frac{{{R_2}}}{{{R_1}}}} \right) = n$
D${\left( {\frac{{{R_1}}}{{{R_2}}}} \right)^{1/2}} + {\left( {\frac{{{R_2}}}{{{R_1}}}} \right)^{1/2}} = {n^{1/2}}$

Medium

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Solution

d
${R_S} = {R_1} + {R_2}$

${R_P} = \frac{{{R_1}{R_2}}}{{{R_1} + {R_2}}}$

$==>$ $\frac{{{R_S}}}{{{R_P}}} = \frac{{{{({R_1} + {R_2})}^2}}}{{{R_1}{R_2}}} = n$$==>$$\frac{{{R_1} + {R_2}}}{{\sqrt {{R_1}{R_2}} }} = \sqrt n $

$==>$$\frac{{\sqrt {R_1^2} }}{{\sqrt {{R_1}{R_2}} }} + \frac{{\sqrt {R_2^2} }}{{\sqrt {{R_1}{R_2}} }} = \sqrt n $

$==>$ $\sqrt {\frac{{{R_1}}}{{{R_2}}}} + \sqrt {\frac{{{R_2}}}{{{R_1}}}} = \sqrt n $

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