Question 2014.S3.38: A separately excited 300 V DC shunt motor under no load runs......

Given that V = 300 R_{a}\,=\,0.5\,\,\Omega N_{0}=900\;\mathrm{rpm},\;I_{a0}=2\,\mathrm{A},\,I_{a1}=15\,\mathrm{A}

Under no load condition:

E_{\mathrm{b0}}=V-I_{\mathrm{a0}}\,R_{\mathrm{a}}=300-(2)(0.5)=299\,\,V

Under load condition:

E_{\mathrm{b1}}=300-I_{\mathrm{al}}R_{\mathrm{a}}=300-(15)(0.5)=292.5~\mathrm{V}

We know that

\frac{N_{1}}{N_{0}}=\frac{E_{\mathrm{bl}}}{E_{\mathrm{b0}}}\Rightarrow N_{1}=\frac{292.5}{299}\times900=880\;\mathrm{rpm}