6) The terminal voltage vB(t), and the terminal current iB(t), for the device sh

Question

6) The terminal voltage vB(t), and the terminal current iB(t), for the device shown in Figure P1.4a are changing with time. Plots of these two variables are shown in Figures P1.4b and P1.4c.

Calculate the energy delivered by this device during the time interval
1[s] < t < 6[s].
alculate the energy delivered by this device during the time interval
1[s] < t < 6[s].
i found the equations for vB(t) and iB(t) and used to find power delivered since device is using active sign convention, then integrated each segment but my answer is wrong with the sign. it should be -41.67[J], but i got +41.67 [J]. i'm not sure where i went wrong.

for 1<t<3 i got

P(t) = -4t^2 + 16t - 7

for 3<t<4 i got

P(t) = 5

for 4<t<5 i got

P(t) = -8t^2 +82t - 195

for 5<t<6 i got

P(t) = -10t +65

Explanation / Answer

See here, the source is feeding energy to the source;hence,it should be negative. You should consider negative sign from the beginning itself, Had device fed the energy to source, then it would have been positive. This is general convention that work done on the system is negative and work done by the system is positive. This is why enrgy supplied to the deive should be negative.

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