Question

The voltage M(t) across a device and the current (t) through it are

V(t)=24cos(2t)V, and xt)=27(1−e −0.5t)mA
Problem 01.014.b - Calculating instantaneous power in a device Calculate the power consumed by the device at
t=1 s. The power consumed by the device at t=1 s is mW.

Answer 1

The power consumed by the device is given by the product of the voltage across the device and the current through it:

P(t) = V(t) * I(t)

We can substitute the given expressions for V(t) and I(t) into this equation to get the power consumed by the device as a function of time:

P(t) = 24cos(2t) * 27(1−e −0.5t)

To find the power consumed by the device at t = 1 s, we can substitute t = 1 into the expression for P(t):

P(1) = 24cos(2 * 1) * 27(1 − e^(-0.5 * 1))

Evaluating this expression, we get:

P(1) = 24cos(2) * 27(1 - e^(-0.5)) = 24 * 27 * (-0.3934693402873666) = -201.24 mW

So, the power consumed by the device at t = 1 s is -201.24 mW. Note that the negative sign indicates that the device is operating in a dissipative mode, meaning that it is consuming power rather than generating power.