In the resistor ladder network shown, current through 3$\mathrm{\Omega }$ resistor is 2A. The emf of the ideal battery is equal to

Use current division rule in parallel combination of resistors Simplified circuit diagram

$\begin{array}{l}{\mathrm{i}}_{\text{net }}=2\mathrm{A}+2\mathrm{A}=4\mathrm{A}\\ {\mathrm{R}}_{\text{net }}=2+1+\frac{3}{2}=4.5\mathrm{\Omega }\\ \mathrm{V}={\mathrm{i}}_{\text{net }}{\mathrm{R}}_{\text{net }}=4\times 4.5=18\mathrm{V}\end{array}$