(a) 'Current is a scalar quantity, although we represent current with an arrow.' Explain. (b) Derive the balance condition of a Wheatstone Bridge.

In the balanced condition, the current $\displaystyle I_{g}$ through G is 0. Then $\displaystyle \mathrm{I}_{1}=\mathrm{I}_{3}$ and $\displaystyle \mathrm{I}_{2}=\mathrm{I}_{4}$

For loop ADBA: $\displaystyle -\mathrm{I}_{1} \mathrm{R}_{1}+0+\mathrm{I}_{2} \mathrm{R}_{2}=0$, or $\displaystyle \dfrac{\mathrm{I}_{1}}{\mathrm{I}_{2}}=\dfrac{\mathrm{R}_{2}}{\mathrm{R}_{1}}\quad \ldots(1)$

For loop CBDC, using $\displaystyle \mathrm{I}_{3}=\mathrm{I}_{1}$ and $\displaystyle \mathrm{I}_{4}=\mathrm{I}_{2}$: $\displaystyle \mathrm{I}_{2} \mathrm{R}_{4}+0-\mathrm{I}_{1} \mathrm{R}_{3}=0$, or $\displaystyle \dfrac{\mathrm{I}_{1}}{\mathrm{I}_{2}}=\dfrac{\mathrm{R}_{4}}{\mathrm{R}_{3}}\quad \ldots(2)$

From ($\displaystyle 1$) and ($\displaystyle 2$): $\displaystyle \dfrac{\mathrm{R}_{2}}{\mathrm{R}_{1}}=\dfrac{\mathrm{R}_{4}}{\mathrm{R}_{3}}$