If current in inductor of inductance 5 mH is varying as I = t 2 e -2 t then find time after which voltage drop across inductor becomes becomes zero.

Question

If current in inductor of inductance 5 mH is varying as I = t 2 e -2 t then find time after which voltage drop across inductor becomes becomes zero. (A) t = 1 sec (B) t = 3 sec (C) t = 2 sec (D) t = 4 sec

Tardigrade Admin · Accepted Answer

Relation between voltage and current in inductance circuit is given by

V_{0} L \frac{d I}{d l} N o w I = t^{2} e^{- 2 t}

V_{0} = - L \frac{d ^{(t^{2} e^{- 2 t})}}{d l}

According to question

0 L \frac{d}{d t}^{(t^{2} e^{2 t})} = - (2 t e^{- 2 t} + (- 2) e^{- 2 t} t^{2})

= 2 e^{- 2 t} t (1 - t) = 0 \Rightarrow t = 1 s

Q. If current in inductor of inductance 5mH is varying as I=t2e−2t then find time after which voltage drop across inductor becomes becomes zero.

t = 1 sec

t = 3 sec

t = 2 sec

t = 4 sec

Relation between voltage and current in inductance circuit is given by V0​LdldI​NowI=t2e−2t V0​=−Ldld(t2e−2t)​ According to question 0Ldtd​(t2e2t)=−(2te−2t+(−2)e−2tt2) =2e−2tt(1−t)=0⇒t=1s

Q. If current in inductor of inductance $5 m H$ is varying as $I = t^{2} e^{- 2} t$ then find time after which voltage drop across inductor becomes becomes zero.