Question

A resistor of 8 ohm is connected in parallel with another resistor X. The resultant resistance of the combination is 4.8 ohm. What is the value of resistor X

Answer 1

Given :

▪ Two resistors of resistance 8Ω and XΩ are connected in parallel.

▪ Eq. resistance of combination = 4.8Ω

To Find :

▪ Value of X

Formula :

→ Formula of equivalent resistance for parallel connection is given by

$\bigstar\:\underline{\boxed{\bf{\red{\dfrac{1}{R_{eq}}=\dfrac{1}{R_1}+\dfrac{1}{R_2}}}}}$

Calculation :

$\dashrightarrow\sf\:\dfrac{1}{R_{eq}}=\dfrac{1}{R_1}+\dfrac{1}{R_2}\\ \\ \dashrightarrow\sf\:\dfrac{1}{4.8}=\dfrac{1}{8}+\dfrac{1}{X}\\ \\ \dashrightarrow\sf\:\dfrac{1}{X}=\dfrac{1}{4.8}-\dfrac{1}{8}\\ \\ \dashrightarrow\sf\:X=\dfrac{8\times 4.8}{8-4.8}\\ \\ \dashrightarrow\sf\:X=\dfrac{38.4}{3.2}\\ \\ \dashrightarrow\underline{\boxed{\bf{\green{X=12\Omega}}}}\:\red{\bigstar}$