# Transient Power Analysis in Electric Circuits

The voltage and current at the terminals of the circuit elements in Fig 1.5 are zero for t<0 nad t<40s. In the interval between 4 and 40s the expressions are:

(a) At what instant of time is the power being delivered to the circuit element maximum?

(b) What is the power at the time found in part (a)

(c) At what instant of time is the power being extracted from the circuit element maximum?

(d) What is the power at the time found in part (b)

(e) Calculate the net energy delivered to the circuit at 0, 10, 20, 30, and 40 s.

Please see attached for circuit diagram.

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#### Solution Preview

The power in a circuit element is voltage times current (P=VI)

The diagram indicates passive sign convention for the element, which means that:

When power is delivered to the element, the power is positive.

When power is extracted from the element, the power is negative.

To find the power, multiply the expressions for v and i

P = v*i = t(1-0.025t)(4-0.2t)

expand the terms:

P = ...

#### Solution Summary

This solution identifies the answer by discussing three key concepts of sign conventions, optimization (maximization and minimization), and power calculations. Detailed explanations and calculations are given.