Question

Calculate the equivalent resistance when two resistances of 3 ohms and 6 ohms are connected in parallel
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Answer 1

Given :

R₁ = 3 ohms

R₂ = 6 ohms

they are connected in parallel

To find :

the equivalent resistance

Solution :

the reciprocal of the combined resistance of a number of resistance connected in parallel is equal to the sum of the reciprocals of the individual resistances. .i.e.,

${\bf {:\implies{ \dfrac{1}{R} = \dfrac{1}{R_1} + \dfrac{1}{R_3} }}}$

${: \implies{\sf{ \dfrac{1}{R} = \dfrac{1}{3} + \dfrac{1}{6} }}}$

${ :\implies{ \sf{ \dfrac{1}{R} = \dfrac{2 + 1}{6} }}}$

${ :\implies{ \sf{ \dfrac{1}{R} = \dfrac{3}{6} }}}$

${ :\implies{ \sf{ \dfrac{1}{R} = \dfrac{1}{2} }}}$

${: \implies{\boxed{\bf R = 2Ω}}}$

thus, the equivalent resistance is 2Ω.

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