Question

three resistors 8 ohm 4 ohm and 10 ohm connected in parallel find the equivalent resistance​

Answer 1

GIVEN :-

• Three resistors of 8Ω , 4Ω and 10Ω are connected in parallel.

TO FIND :-

• Equivalent Resistance (R').

TO KNOW :-

For Parallel Combination,

$\\ \large \dagger \boxed{ \sf \: \frac{1}{R'} = \frac{1}{ R_{1} } + \frac{1}{R_{2}} + \frac{1}{R_{3}} + \dots + \frac{1}{R_{n}} }$

Here ,

• R' is Equivalent Resistance.
• R(1) , R(2) , R(3) are resistors in parallel combination.

SOLUTION :-

We have ,

• R(1) = 8Ω
• R(2) = 4Ω
• R(3) = 10Ω

Putting values in formula,

$\\ \implies\sf \: \dfrac{1}{R'} = \dfrac{1}{8} + \dfrac{1}{4} + \dfrac{1}{10} \\ \\ \\ \implies \sf \: \dfrac{1}{R'} = \dfrac{1(5) + 1(10) + 1(4)}{40} \\ \\ \\ \implies \sf \: \dfrac{1}{R'} = \dfrac{5 + 10 + 4}{40} \\ \\ \\ \implies \sf \: \dfrac{1}{R'} = \dfrac{19}{40} \\ \\ \\ \implies \boxed{\sf \: R' = \dfrac{40}{19}\Omega}$

Hence , Equivalent Resistance is 40/19Ω.

MORE TO KNOW :-

For Series Combination,

★ R' = R(1) + R(2) + R(3) ... + R(n)