24Ω
When resistors are connected in parallel, the reciprocal of their combined resistance, when read with a DMM (Digital Multimeter - for measuring various properties of a circuit or circuit element such as resistance...) is the sum of the reciprocals of their individual resistances.
For example if two resistors of resistances R₁ and R₂ are connected together in parallel, the reciprocal of their combined resistance Rₓ is given by;
[tex]\frac{1}{R_x}[/tex] = [tex]\frac{1}{R_1}[/tex] + [tex]\frac{1}{R_2}[/tex]
Solving for Rₓ gives;
[tex]R_{x}[/tex] = [tex]\frac{R_1 * R_2}{R_1 + R_2}[/tex] ------------------(i)
From the question;
Let
R₁ = resistance of first resistor = 40Ω
R₂ = resistance of second resistor = 60Ω
Now,
To get their combined or total resistance, Rₓ, substitute these values into equation (i) as follows;
[tex]R_{x}[/tex] = [tex]\frac{40 * 60}{40 + 60}[/tex]
[tex]R_{x}[/tex] = [tex]\frac{2400}{100}[/tex]
[tex]R_{x}[/tex] = 24 Ω
Therefore, the total resistance is 24Ω
