Answer :

483 (Range : 480 to 485)

We know that, for separately excited DC motor

T∝ ϕ Ia

As we know that in separately excited machines we generally consider as constant

⇒ T∝ Ia

∴ $\frac{T_2}{T_1}=\frac{I_{a2}}{I_{a\mathrm{1 }}}$

$\frac{{\mathrm{}}_{}}{}$Now, given that T∝ N

⇒$\frac{T_2}{T_1}=\frac{N_2}{N_1}$

$\frac{{\mathrm{\Rightarrow \; I}}_{a2}}{I_{a1}}=\frac{N_2}{N_1}$

$\frac{{\mathrm{}}_{}}{}$It is given that

I_a1=30A and N₁=1000rpm

⇒ $I_{a2}=\frac{30}{1000}{N}_2=0.03N_2$

$\mathrm{And,\; we\; know\; that,}$

$N\propto \frac{E_f}{\varphi }$

$\frac{}{}$$\frac{N_2}{N_1}=\frac{E_2}{E_1}$

$\frac{N_2}{N_1}=\frac{V-I_{a2}(R_a+R_{ext})}{V-I_{a1}{R}_a}$

$\Rightarrow \frac{N_2}{1000}=\frac{280-0.03N_2(1+10)}{280-30(1)}=\frac{280-0.33N_2}{250}$

$\frac{\mathrm{}}{}$250 × N2=280 × 1000 - 330 N2

∴ N2=482.76 rpm