EE 2400

The Passive Sign Convention

AndConservation of Power

This powerpoint presentation was prepared by Dr. Lloyd A.

“Pete” MorleyThe University of Alabama

2005

The Passive Sign ConventionConsider the following circuit:

ele-ment

a+

b

I

V

If the reference direction of the current (i.e., the direction the arrow is pointing) is from the + side of the voltage reference through the element to the - side of the voltage reference, then …

ele-ment

a+

b

I

V

P=VI and a value of P > 0 signifies that power is being absorbed by the element while a value of P < 0 signifies that power is being provided by the element.This is called the passive sign convention.

Proving the Passive Sign Convention

ele-ment

a+

b

I

V

Let’s prove and understand this concept by looking at each of the four possible cases for V and I and considering conservation of energy within the circuit.

ele-ment

a+

b

I

V

Case 1: V > 0 and I > 0The physics: Since I is positive, charge moves from point a through the element to point b. Since V is positive, charge at point a has a higher level of energy than charge at point b. The charge thus loses energy as it travels from a to b through the element, and this energy (or power) must be absorbed by the element.

Proving the Passive Sign Convention (cont.)

ele-ment

a+

b

I

V

Case 2: V > 0 and I < 0The physics: Since I is negative, charge moves from point b through the element to point a. Since V is positive, charge at point a has a higher level of energy than charge at point b. The charge thus gains energy as it travels from b to a through the element, and this energy (or power) must be provided by the element.

Proving the Passive Sign Convention (cont.)

ele-ment

a+

b

i(t)

v(t)

Case 3: V < 0 and I > 0Case 4: V < 0 and I < 0You work these two cases right now on your own paper.

Proving the Passive Sign Convention (cont.)

Conservation of PowerFor complete circuits, the sum of all powers generated and absorbed is zero (i.e., circuit exhibits conservation of energy and conservation of power)Power generated = Power

absorbed

ele-ment

a+

b

I

V

Case 3: V < 0 and I > 0The physics: Since I is positive, charge moves from point a through the element to point b. Since V is negative, charge at point b has a higher level of energy than charge at point a. The charge thus gains energy as it travels from a to b through the element, and this energy (or power) must be provided by the element.

Proving the Passive Sign Convention (cont.)

ele-ment

a+

b

I

V

Case 4: V < 0 and I < 0The physics: Since I is negative, charge moves from point b through the element to point a. Since V is negative, charge at point b has a higher level of energy than charge at point a. The charge thus loses energy as it travels from b to a through the element, and this energy (or power) must be absorbed by the element.

Proving the Passive Sign Convention (cont.)