For the long shunt compound generator shown in the figure, the ratio \(\frac{\mathrm{I}_{\mathrm{sh}}}{\mathrm{I}_{\mathrm{a}}}\) is :

Concept

\(I_a=I_{sh}+I_L\)

where, I_a = Armature current

I_sh = Shunt winding current

I_L = Load current

Calculation

\(\frac{\mathrm{I}_{\mathrm{sh}}}{\mathrm{I}_{\mathrm{a}}}={I_a-I_L\over I_a}\)

\(\frac{\mathrm{I}_{\mathrm{sh}}}{\mathrm{I}_{\mathrm{a}}}=1-{I_L\over I_a}\)

Since the armature current (I_a) is the sum of Ish and I_L. 

∴  Ia > I_L ⇒ \(0<{I_L\over I_a}<1\)

\(0<(1-{I_L\over I_a})<1\)

So, the ratio of \(\frac{\mathrm{I}_{\mathrm{sh}}}{\mathrm{I}_{\mathrm{a}}}\) will always less than 1.