Question

The equivalent resistance of two resistors connected in series is 6 ohm and their parallel equivalent resistance is 4/3. what are the value of resistors​

Answer 1

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The equivalent resistance of two resistors connected in series is 6 ohm and their parallel equivalent resistance is 4/3. what are the value of resistors

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$\red{Let \ the \ resistances \ be :}$

• $R_1$
• $R_2$

$\star {\pink{\tt{\underline{\sf{Resistance \ in \ series}}}}}$

$\red{\implies}R_1 + R_2 = 6 \Omega$

$\red{\implies}R_2 = 6 - R_1$

$\star {\pink{\underline{\tt{\sf{Resistance \ in \ parallel}}}}}$

$\blue{\implies}\dfrac{1}{R_1} + \dfrac{1}{R_2} = \dfrac{3}{4}$

$\blue{\implies}\dfrac{R_1 + R_2}{R_1R_2} = \dfrac{3}{4}$

$\blue{\implies}\dfrac{\red{6}}{R_1(6 - R_1)} = \dfrac{3}{4}$

$\blue{\implies}\dfrac{6}{6R_1 - {R_1}^2} = \dfrac{3}{4}$

$\green{\implies}6 \times 4 = 3 (6R_1 - {R_1}^2)$

$\green{\implies}24 = 18 R_1 - 3 {R_1}^2$

$\green{\implies} {R_1}^2 - 6R_1 + 8 = 0$

$\green{\implies} {R_1}^2 - 4R_1 - 2R_1 + 8 = 0$

$\green{\implies}R_1(R_1 - 4) - 2(R_1 - 4) = 0$

$\green{\implies}(R_1 - 2)(R_1 - 4) = 0$

$\green{\boxed{\implies{\boxed{R_1 = 4\ or\ 2}}}}$

$\green{\boxed{\implies{\boxed{R_2 = 6 - R_1 = 6 - 4\ or\ 6 - 2 = 2 \ or\ 4}}}}$

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