0195136047.pdf

24 CIRCUIT CONCEPTS

currentiLis then equal to the short-circuit current of the sourcei. Hence, it is desirable to have

as large an internal resistance as possible in a practical current source.

Capacitance

Anideal capacitoris an energy-storage circuit element (with no loss associated with it) repre-

senting the electric-field effect. The capacitance in farads (F) is defined by

C=q/v (1.2.16)

whereqis the charge on each conductor, andvis the potential difference between the two

perfect conductors. Withvbeing proportional toq,Cis a constant determined by the geometric

configuration of the two conductors. Figure 1.2.5(a) illustrates a two-conductor system carrying

+qand−qcharges, respectively, forming a capacitor.

The general circuit symbol for a capacitor is shown in Figure 1.2.5(b), where the current

entering one terminal of the capacitor is equal to the rate of buildup of charge on the plate

attached to that terminal,

i(t)=

dq

dt

=C

dv

dt

(1.2.17)

in whichCis assumed to be a constant and not a function of time (which it could be, if the

separation distance between the plates changed with time).

The terminalv–irelationship of a capacitor can be obtained by integrating both sides of

Equation (1.2.17),

v(t)=

1

C

∫t

−∞

i(τ) dτ (1.2.18)

which may be rewritten as

v(t)=

1

C

∫t

0

i(τ) dτ+

1

C

∫^0

−∞

i(τ) dτ=

1

C

∫t

0

i(τ) dτ+v( 0 ) (1.2.19)

wherev(0) is theinitialcapacitor voltage att=0.

The instantaneous power delivered to the capacitor is given by

p(t)=v(t)i(t)=C v(t)

dv(t)

dt

(1.2.20)

whose average value can be shown (see Problem 1.2.13) to be zero for sinusoidally varying current

and voltage as a function of time. The energy stored in a capacitor at a particular time is found

by integrating,

A

B AB

+q charge

Potential vA

−q charge

Potential vB

Potential difference = v = vA − vB; C = q/v

i(t) C

v(t)

(a) (b)

i(t) == C ;

dq

dt C

v(t)^1

=

dv

dt ∫i(τ) dτ

t

C

=^1

+−

∫i(τ) dτ + v(0)

0

t

Figure 1.2.5 Capacitor.(a)Two perfect conductors carrying+qand−qcharges.(b)Circuit symbol.