Question

(c) The equivalent resistance of two unknown resistors when they are connected in
parallel is 15 Ohm While connecting them in series the equivalent resistance is 60 Ohm
What is the resistance of those two resistors?

Answer 1

Let the two resistors be R1 and R2.

Given

$\bullet \: \tt R_1 + R_2 = 60 \: \: \: \: \: \: ....(1)$

$\bullet \: \tt \dfrac{R_{1}R_{2}}{R_1 + R_2} = 15\: \: \: \: \: \: ....(2)$

$\implies \tt R_1R_2 = 15 \times 60$

$\implies \tt R_1R_2 = 900$

$\tt \implies R_2 = \dfrac{900}{R_1}$

$\tt \: R_1 + \dfrac{900}{R_1} = 60$

$\tt \implies\: R_1 ^{2} + 900 = 60R_1$

$\tt \implies\: R_1 ^{2} - 60R_1+ 900 = 0$

$\tt \implies\: R_1 ^{2} - 30R_1 - 30R_1+ 900 = 0$

$\tt \implies\: R_1 ( R_1 - 30) - 30(R_1 - 30) = 0$

$\tt \implies\: ( R_1 - 30) (R_1 - 30) = 0$

$\bf \tt \: R_1 = 30 \ ohm$

$\bf \tt \: R_2 = 30 \ ohm$