Bridging Circuits and Fields

CHAPTER 2 Power Theory in Electrical Circuits

1. Introduction

Defining the concept of power means opening a can of ‘scientific worms’.

Griffiths (2013:357) defines power as the rate of work:

$Power=\frac{dW}{dt}={\displaystyle {\int }_v\left(E\cdot J\right)dt}$

where work or energy E · J is deployed in per unit (p.u.) time and volume (i.e., energy has both time and space attributes).

However, Lehrman wrote a paper entitled “Energy is Not the Ability to Do Work” (Lehrman, 1973).

Valkenburg (1964) defines power as only a time-derivative of energy:

$p=\frac{dw}{dt}$

He factorizes the expression for the time derivative of energy into a product of voltage and current:

$\frac{dw}{dt}=\frac{dw}{dq}\times \frac{dq}{dt}=v\cdot i$

Einstein’s definition of energy

$E=m{c}^2$

has long been ...