Physics - Current Electricity Question with Solution | TestHub

Let$\mathrm{x}$be the equivalent resistance of the infinite ladder then,

the equivalent circuit is



also, the equivalent resistance is

$\mathrm{x}=1+\frac{2\mathrm{x}}{2+\mathrm{x}}$

${\mathrm{x}}^2-\mathrm{x}-2=0$

$\mathrm{x}=\frac{1+\sqrt{1+8}}{2}=2\mathrm{ }\mathrm{\Omega }$

current through the battery is$3\mathrm{ }\mathrm{A}$.



Current through$2\mathrm{ }\mathrm{\Omega }$resistor is

$\mathrm{i}=3\left(\frac{\mathrm{x}}{2+\mathrm{x}}\right)=3\left(\frac{2}{2+2}\right)=1.5\mathrm{ }\mathrm{A}$