Question

The effective resistivity resistance of the parallel
combination of two resisters of 60-2 and 40-2
is..... options: a) 100Ω b) 50Ω c) 24 Ω d) 2400Ω​

Answer 1

Given :

Two resistors are connected in parallel combination.

• R₁ = 60Ω
• R₂ = 40Ω

To find :

The effective resistance

Solution :

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

${ \boxed{ \bf{\dfrac{1}{R} = \dfrac{1}{R_1} + \dfrac{1}{R_2}}}}$

by substituting value in the formula,

${ \leadsto{ \sf{\dfrac{1}{R} = \dfrac{1}{R_1} + \dfrac{1}{R_2}}}}$

${ \leadsto{ \sf{\dfrac{1}{R} = \dfrac{1}{60} + \dfrac{1}{40}}}}$

${ \leadsto{ \sf{\dfrac{1}{R} = \dfrac{2 + 3}{120} }}}$

${ \leadsto{ \sf{\dfrac{1}{R} = \dfrac{5}{120} }}}$

${ \leadsto{ \sf{\dfrac{1}{R} = \dfrac{1}{24} }}}$

${ \leadsto{ \sf{{R} = 24 \: \Omega }}}$

thus, Option (c) 24Ω is correct.