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