Question

An 8-pole, 200 V shunt excited dc generator has a lap wound armature having 100 coils of 8 turns. The resistance of each conductor is 0.025 $\Omega$ and field winding resistance is 100 $\Omega$. If total core and mechanical losses are 1250 W. The current at maximum efficiency is _________

• A. 51.38

Answer 1

The correct option is A 51.38
$\text{For maximum efficiency,}$
$\text{Variable losses = Constant losses}$

$I_a^2{R}_a=P_k$

$I_a=\sqrt{\frac{P_k}{R_a}}...\left(i\right)$

$\text{Constant losses for dc machine is}$
$P_k=\text{(core+mech)loss +field losses}$

$=1250+\frac{{200}^2}{100}=1650W$

$\text{Armature resistance (}{R}_a\text{) :}$

$\text{Conductor per path =}\frac{100\times 8\times 2}{8}=200$

$\text{Resistance per path =}200\times 0.025\Omega$

$\text{Total armature resistance =}\frac{200\times 0.025}{8}=0.625\Omega$

$\text{From equation (i), we get}$

$I_a=\sqrt{\frac{1650}{0.625}}=51.38A$