PRACTICAL MATLAB® FOR ENGINEERS PRACTICAL MATLAB

Direct Current and Transient Analysis 107

R.2.33 Electric power is defi ned as the rate of generating or consuming (dissipating) energy.

Electric power (denoted by P) is defi ned as the product of a voltage across, and the

resulting current through an element. The unit of electric power is watt (W). Then

P (W) = current (A) * voltage (V)

or

P (W) = energy/time ( J/s)

The power of 1 W implies a rate of generating or consuming 1 J of energy per

second (s).

R.2.34 Decibel (denoted by dB) is the unit used to express powers, voltages, and currents

as ratios. Decibel is defi ned as

dB = 10 log 10 [PO/PI]

dB = 20 log 10 [VO/VI]

and

dB = 20 log 10 [IO/II]

Strictly speaking, a decibel can be used to express only ratios, which is a measure

of losses, gains, or no changes. The subscripts “O” and “I” denote output and input,

respectively. For example, PO/PI denotes output power divided by input power

referred to as power gain.

R.2.35 Electrical energy (denoted by W) is the amount of power generated or consumed

during a given interval of time [t 0 , t 1 ] of interest.

Therefore,

Wptdt

t

t

(J)
 ()

0

1

∫

is often expressed in terms of watts * hours (W h), especially by the utilities

companies.*

R.2.36 The principle of conservation of energy states that

energy can be transformed, but never destroyed.

E l e c t r i c a l e n e r g y c a n b e t r a n s f o r m e d i n t o m e c h a n i c a l e n e r g y (m o t o r) a n d v i c e v e r s a

(generator) or any other form of energy such as nuclear, thermal, and hydraulic.

The following relations indicate the equivalency between mechanical and elec-

trical units of energy often used in practice:

1 J = 0.737 ft ⋅ lbf

1ft ⋅ lbf = 1.357 J

1 Btu = 1055 J

1 Hp = 746 W = 550 ft ⋅ lbf/s

*^ The reader should not confuse P (W), that is the power given in watts with W (J), that is the energy given in

Joules, where W = J/s (Watt = Joule/sec).