The resistance of the series combination of two resistance is S. When they are joined in parallel the total resistance is P. If S =

Q: The resistance of the series combination of two resistance is $S$. When they are joined in parallel the total resistance is $P$. If $S = nP$, then the minimum possible value of $n$ is

a (a) If two resistances are ${R_1}$ and ${R_2}$ then $S = {R_1} + {R_2}$ and $P = \frac{{{R_1}{R_2}}}{{({R_1} + {R_2})}}$ From given condition $S = nP$ i.e. $({R_1} + {R_2}) = n\,\left( {\frac{{{R_1}{R_2}}}{{{R_1} + {R_2}}}} \right)$ $==>$ ${({R_1} + {R_2})^2} = n\,\,{R_1}{R_2}$ $==>$ ${({R_1} - {R_2})^2} + 4{R_1}{R_2} = n{R_1}{R_2}$ So $n = 4 + \frac{{{{({R_1} - {R_2})}^2}}}{{{R_1}{R_2}}}.$ Hence minimum value of $n$ is $4$.

SECTION - A [PHYSICS - MCQ]

GSEB - English Medium

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

A$4$
B$3$
C$2$
D$1$

AIEEE 2004,JEE MAIN 2021, Diffcult

STD 11 Science
NEET
STD 12 - 3. current electricity
Physics

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