The overall current flowing through the above circuit is 9 A. If the voltage is 12 V and the resistance of the resistor R₁ = 4 $\Omega$. Find the resistance of resistor R₂.

The overall current in the circuit = 9A (Given)

The voltage is 12 𝑉 (Given) 

Hence by Ohm’s Law, 𝑉 = 𝐼R

The resistance for the entire circuit is

$$\begin{gathered} \mathrm{R}=\frac{12}{9} \\ \Rightarrow \mathrm{R}=\frac{4}{3}\mathrm{\Omega } ......... \left(\mathrm{a}\right) \end{gathered}$$

${\mathrm{R}}_1\text{ and }{\mathrm{R}}_2\text{ are in parallel. }$

$\text{ Therefore, }\mathrm{R}=\frac{\left({\mathrm{R}}_1{\mathrm{R}}_2\right)}{\left({\mathrm{R}}_1+{\mathrm{R}}_2\right)} .......... \left(\mathrm{b}\right)$

Putting the value of 𝑅 = $4\Omega$(Given) in equation (b)

$\Rightarrow \mathrm{R}=\frac{4{\mathrm{R}}_2}{\left(4+{\mathrm{R}}_2\right)} ........ \left(\mathrm{c}\right)$

Putting the value of 𝑅 from equation (a) in equation (c)

$\Rightarrow \frac{4}{3}=\frac{4{\mathrm{R}}_2}{\left(4+{\mathrm{R}}_2\right)}$

$\Rightarrow 16+4{\mathrm{R}}_2=124{\mathrm{R}}_2$

$\Rightarrow {\mathrm{R}}_2=2\mathrm{\Omega }$