Page 114 - MATLAB an introduction with applications

Electrical Circuits ——— 99

The energy stored in an inductance is

1 1
E = Li = L ( q ) 2
2
2 2
where q is the electrical charge.
The voltage drop in an inductance is

V i = Li = L q
Inductances in Series: Since the voltage drop through an inductor is proportional to the inductance L, we
have (Fig. 2.4 (a))

L eq = L 1 + L 2
L 1
L 1 L 2

L 2
(a) Inductances in series (b) Inductances in parallel
Fig. 2.4 Inductances

Inductances in Parallel: Referring to Fig. 2.4 (b), we have
LL
L eq = 12
L + L 2
1
Similarly, for n inductors
1 = 1 + 1 + ... + 1
L eq L 1 L 2 L n
Capacitance Elements: Capacitance C is a measure of the quantity of charge that can be stored for a given
voltage across the plates. The capacitance C of a capacitor is given by
q
C =
V c
where q is the quantity of charge stored and V c is the voltage across the capacitor.
dq
Since i = and V c = q/C, we have
dt
dV
i = C c
dt
1
or dV c = i dt
C
1
Hence V c = ∫i c dt
C

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