## anonymous 5 years ago 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)

1. anonymous

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

2. anonymous

$I=\int\limits_{}^{}1000(0.5^2e ^{-500t})dt=\int\limits_{}^{}250e ^{-500t}dt$ $=-0.5e ^{-500t}$ 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

3. anonymous

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 )

4. anonymous

oh sorry I forgot the minus in the power

5. anonymous

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

6. anonymous

sorry for the typo mistake

7. anonymous

does that make sense to you?

8. anonymous

Yes.Thank you !!!

9. anonymous

np