PRACTICAL MATLAB® FOR ENGINEERS PRACTICAL MATLAB

Direct Current and Transient Analysis 115

For the case of n inductors L 1 , L 2 , L 3 , ..., Ln connected in parallel, the equivalent

inductor Leq is given by

11

LLi 1 i

n

eq

∑

or

L

i Li

eq
 n

1

∑ 1 (/ )^1

R.2.60 Recall that the electric power dissipated by a resistor R, with voltage V across it,

and a current I fl owing through it is given by

P = I * V = I^2 * R = V^2 /R (W)

During an interval of time T, the energy (WR) dissipated by a resistor R is given by

WR = P (^) T = I (^) V (^) T = (V^2 /R) T = I^2 R (^) T (J)
R.2.61 An ideal inductor with no (zero) resistance cannot dissipate energy; it can only
store energy. The energy stored in an inductor L is given by
WtL()
L itJ)

1

2

2

* ()(

For the DC case (constant current I), the energy is given by

WLIL

1

2

*^2

* ()J

R.2.62 An ideal capacitor with no (zero) resistance cannot dissipate energy; it can only

store energy in its electric fi eld. Its energy is given by

WCvtC

1

2

2

**()(J)

For the DC case (constant voltage V), the energy is given by

WCVC

1

2

2

* ()J

R.2.63 In a DC circuit, the steady-state voltage drop across an inductor L is 0 V since

vt L

di t

L dt

()

()