Derive a power balance equation for the RL and RC

QUESTION:

Derive a power balance equation for the 𝑅𝐿 and 𝑅𝐶 circuits. (See Problem 5.) Discuss the significance of the signs of the three power terms.

The power generated or dissipated by a circuit element equals the voltage across the element times the current through the element. Show that the power dissipated by a resistor equals \(I^{2} R\), the power associated with an inductor equals the derivative of \((1 / 2) L I^{2}\), and the power associated with a capacitor equals the derivative of \((1 / 2) C E_{C}^{2}\).

Equation Transcription:

Text Transcription:

I^{2}R

(1/2)LI^{2}

(1/2)CE_{C}^{2}