GATE 2015 EE – SET 1 – Question 21

Solution :

$$R_{a}$$ = 0.152 , $$E_{1} $$= 200 V , Rate speed =$$ N_{1}$$ , Rate flux = $$\phi _{1}$$

Half  rated speed =$$ N_{2}$$ = $$\frac{N_{1}}{2}$$

Half rated flux =  $$\phi _{2}$$  ⇒  $$\phi _{2}$$ = $$\frac{\phi _{1}}{2}$$

$$E\alpha$$ = $$\phi N$$

$$\frac{E_{1}}{E_{2}} $$= $$\frac{\phi _{1}N_{1}}{\phi _{2}N_{2}}$$

$$E_{2}$$ = 200 /4 = 50 V

E =V $$\left \lfloor 1 – e^\frac{-t}{RC}\right \rfloor $$

25 = 50 $$\left \lfloor 1 -e^\frac{-t}{0.1*1000*10^{-6}} \right \rfloor$$

$$\frac{1}{2}$$  =$$ 1- e^\frac{-t}{100*10^{-6}}$$

t = 0.693 * 10 -4

t = 69.3 * 10 -6

t = 69.3μs