Question

83. Three conductors having values 2 ohm, 3 ohm and 4 ohm are connected in parallel. Find equivalent resistance.

1) 20 ohm. 2) 9 ohm 3) 13/12ohm 4)12 /13ohm​

Answer 1

Required Answer:-

Here in this question stated that, there are three conductors having values 2 ohm, 3 ohm and 4 ohm are connected in parallel. And we are asked to find out the equivalent resistance. Such that,

• R₁ = 2 Ω
• R₂ = 3 Ω
• R₃ = 4 Ω
• Rₚ = ?

We know that, when three resistance R₁, R₂ and R₃ respectively are connected in a parallel combination then their equivalent resistance Rₚ is given by,

$\bf{\red{\longmapsto\boxed{\bf{\blue{ \frac{1}{R_p}=\frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_3}}}}}}$

Now, by using the equivalent resistance formula and substituting all the given values in it, we get:

➙ 1/Rₚ = 1/2 + 1/3 + 1/4

➙ 1/Rₚ = 6 + 3 + 4/12

➙ 1/Rₚ = 13/12

➙ Rₚ = 12/13 Ω

Therefore, the equivalent resistance is 12/13 Ω. So option (4) is the correct option for this question.

Answer 2

Given :-

Three conductors having values 2 ohm, 3 ohm and 4 ohm are connected in parallel

To Find :-

Equivalent resistance.

Solution :-

As they are connected in parallel. So, equivalent resistance will be -

1/Rn = 1/R1 + 1/R2 + 1/R3

1/Rn = 1/2 + 1/3 + 1/4

1/Rn = 6 + 4 + 3/12

1/Rn = 13/12

12(1) = 13(Rn)

12 = 13Rn

12/13 = Rn