Question

three resistors 3 ohms 12 ohms and 9 ohms are connected in parallel find equivalent resistance. ​

Answer 1

Given :

Three resistors are connected in parallel combination

• R₁ = 3Ω
• R₂ = 12 Ω
• R₃ = 16Ω

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 all the individual resistances that is,

$\boxed{\bf \dfrac{1}{R} = \dfrac{1}{R_1} + \dfrac{1}{R_ 2} + \dfrac{1}{R_3}}$

Substituting all the values in the formula,

$\leadsto{\sf \dfrac{1}{R} = \dfrac{1}{R_1} + \dfrac{1}{R_ 2} + \dfrac{1}{R_3}}$

$\leadsto{\sf \dfrac{1}{R} = \dfrac{1}{3} + \dfrac{1}{12} + \dfrac{1}{9}}$

$\leadsto{\sf \dfrac{1}{R} = \dfrac{12 + 3 + 4}{36}}$

$\leadsto{\sf \dfrac{1}{R} = \dfrac{19}{36}}$

$\leadsto{\sf R = \dfrac{36}{19}}$

$\leadsto{\sf R = 1.89 \: \Omega}$

thus, the equivalent resistance when connected in parallel is 1.89 Ω.

Remember !

SI unit of resistance is ohms (Ω).

Answer 2

Equivalent resistance(1/Rp)=(1/R1)+(1/R2)+(1/R3)
(1/Rp)=(1/3)+(1/12)+(1/9)
(1/Rp)=((3+1)/9)+(1/12)
(1/Rp)=(4/9)+(1/12)
(1/Rp)=(16+3)/36
(1/Rp)=(19/36)
Rp=36/19=1.89 ohms
So the equivalent resistance is 1.89 ohms