Question

A 420 V dc shunt motor takes 6 A at no - load. Its armature resistance (including brushes) is $1\Omega$ and shurt field resistance is $210\text{ohm}$. The effciencey when motor takes 52 A on full load is____%

• A. 78.71

Answer 1

The correct option is A 78.71
Given, $V_t=420V,r_f=210\Omega$
$r_a=1\Omega ,I_{L0}=6A$
$I_{L1}=52A$
Field current $I_f=\frac{420}{210}=2A$
$I_{a0}=6-2=4A$
At no - load back emf developed is
$E_{b0}=(V_t-I_{a0}\times r_a)\propto {\varphi }_0{N}_0$
or, $E_{b0}=(420-(6-2)\times 1)\propto {\varphi }_0{N}_0....\left(i\right)$
Constant non - load rotational loss $=V_t\times I_{a0}-I_{a0}^2{T}_s$
$=420\times 4-(4{)}^2\times 1$
$=1680-16=1664W$
Full load amature copper loss $=I_a^2{r}_a=(50{)}^2\times 1=2500W$
Constant shunt field loss $=V_t\times L_f=420\times 2=840W$
$\therefore$ Total losses at full load $=2500+840+1664=5004W$
Powr input at full load $=52\times 420=21840W$
$\therefore$ Motor efficiency $=(1-\frac{504}{21840})\times 100\%=77.09\%$