Question 16.17: In a shunt DC motor, it is assumed that the magnetic circuit......
In a shunt DC motor, it is assumed that the magnetic circuit is linear. If the applied voltage is halved in the no-load condition, what will be the ratio of the new speed of the motor to the old one?
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1) 0.5
2) 2
3) 1
4) 0.25
Based on the information given in the problem, we have:
φ \propto I_f (1)
V_{t,2}=0.5V_{t,1} (2)
As we know, the induced armature voltage of an electric machine can be determined as follows:
E_{a}=k_1φω\overset{(1)}{\Longrightarrow } E_a=k_aI_f\omega (3)
Figure 16.17 shows the electrical circuit of a shunt DC motor. Applying Ohm’s law for the branch of field winding:
I_f=\frac{V_t}{R_{fc} + R_{fw}}=\frac{V_t}{R_f}\Rightarrow I_f\propto V_t (4)
Solving (3) and (4):
E_a=k_aV_t\omega (5)
Moreover, as we know, in the no-load condition, we have:
E_a\approx V_t (6)
Solving (5) and (6):
k_aV_t\omega=V_t\Rightarrow \omega-\frac{1}{k_a}=\text{Const.}\Rightarrow \pmb{\frac{\omega_2}{\omega_1}=1}
Choice (3) is the answer.
