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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)
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)

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anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0solve the integral in the interval from t=0 to t=0.001

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0\[I=\int\limits_{}^{}1000(0.5^2e ^{500t})dt=\int\limits_{}^{}250e ^{500t}dt\] \[=0.5e ^{500t}\] 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
 5 years ago
Best ResponseYou've already chosen the best response.0My 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
 5 years ago
Best ResponseYou've already chosen the best response.0oh sorry I forgot the minus in the power

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0it will be 0.5(e^(.5)1)=0.197 joules so the energy lost is 197*10^(3)J (answer 2)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0sorry for the typo mistake

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0does that make sense to you?
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