The value of the resistor, R_S , needed in the dc voltage regulator circuit shown here, equals :

$\text{ Total current in resistance }{\mathrm{R}}_{\mathrm{S}} , \mathrm{I}={\mathrm{nI}}_{\mathrm{L}}+{\mathrm{I}}_{\mathrm{L}}=(\mathrm{n}+1){\mathrm{I}}_{\mathrm{L}}$

$\text{ Voltage across }{\mathrm{R}}_{\mathrm{S}}\text{ is }{\mathrm{V}}_{\mathrm{S}}={\mathrm{V}}_{\mathrm{i}}-{\mathrm{V}}_{\mathrm{L}}$

$\therefore {\mathrm{R}}_{\mathrm{S}}=\frac{{\mathrm{V}}_{\mathrm{S}}}{\mathrm{I}}=\frac{{\mathrm{V}}_{\mathrm{i}}-{\mathrm{V}}_{\mathrm{L}}}{(\mathrm{n}+1){\mathrm{I}}_{\mathrm{L}}}$