The equivalent resistance of series combination of two resistors is 's'. When they are connected in parallel, the equivalent resistance is 'p'. If s = np, then the minimum value for n is ____________. (Round off to the Nearest Integer)
Answer (integer)
4
Solution
$s = np$<br><br>${R_1} + {R_2} = n\left[ {{{{R_1}{R_2}} \over {{R_1} + {R_2}}}} \right]$<br><br>$\Rightarrow$ $R_1^2 + R_2^2 + 2{R_1}{R_2} = n{R_1}{R_2}$<br><br>$\Rightarrow$ $R_1^2 + (2 - n){R_1}{R_2} + R_2^2 = 0$
<br><br>For real roots, b<sup>2</sup> - 4ac $\ge$ 0
<br><br> ${[(2 - n){R_2}]^2} - 4 \times 1 \times R_2^2$ $\ge$ 0<br><br>$\Rightarrow$ ${(2 - 4)^2}R_2^2 \ge 4R_2^2$<br><br>$\Rightarrow$ 2 $-$ n $\ge$$\pm$2<br><br>$\Rightarrow$ 2 $-$ n $\ge$ $-$2<br><br>$\Rightarrow$ n $\ge$ 4<br><br> So, minimum value for n = 4
About this question
Subject: Physics · Chapter: Current Electricity · Topic: Ohm's Law and Resistance
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