The current flowing through a 1000 ohm resistor varies according to the equation i=0.5 exp(-250t).If the power consumed by the resistor is equal to the rate at which the energy is used, how much energy is lost in the resistor from t=0 to t=0.001 sec? Hint:w=∫Ri^2dt (use i^2 not i)

Question

The current flowing through a 1000   ohm  resistor varies according to the equation   i=0.5 exp(-250t).If the power consumed by the resistor is equal to the rate at which the energy is used, how much energy is lost in the resistor from t=0 to   t=0.001 sec?                                            Hint:w=∫Ri^2dt  (use i^2 not i)

anonymous · Answer

solve the integral in the interval from t=0 to t=0.001

anonymous · Answer

$$I=\int\limits_{}^{}1000(0.5^2e ^{-500t})dt=\int\limits_{}^{}250e ^{-500t}dt$$
$$=-0.5e ^{-500t}$$
substitute for the interval from t=0 to t=0.001 to get
$$-0.5(e ^{-500(0.001)}-e ^{0})=-0.5(e ^{1/2}-1)$$
therefor the energy lost in the resistor = 0.5(e^0.5 -1)
I hope it's right

anonymous · Answer

My possible answers are; 1) 197*10^(-6) J;  2)197*10^(-3) J;   3)0.86 J;     4)1.234 J ;  5) 1.68 J;     6) 2.756 J    
(All units are in JOULES )

anonymous · Answer

oh sorry I forgot the minus in the power

anonymous · Answer

it will be
-0.5(e^(-.5)-1)=-0.197 joules
so the energy lost is 197*10^(-3)J (answer 2)

anonymous · Answer

sorry for the typo mistake

anonymous · Answer

does that make sense to you?

anonymous · Answer

Yes.Thank you !!!

anonymous · Answer

np