Capacitor

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Capacitor

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Capacitor is a passive element. capacitance (C) is a property of the capacitor by which it stores electrical energy by means of electrostatic stress.Capacitance is measured in Farad. The charge across the capacitor is expressed by

q=cv (20)

As the current is defined by

$\small \mathrm i=\frac{\mathrm{dq}}{\mathrm{dt}}$ (21)

Substituting (20) in equation (21) gives

$\mathrm i=\mathrm C\frac{\mathrm{dv}}{\mathrm{dt}}$ (22)

And $\mathrm v=\frac1{\mathrm C}\int\mathrm{idt}$ (23)

Equation (22) and (23) are the parametric equations of an capacitor.

Series and parallel connections of capacitors: Two or more capacitors can be connected in series or parallel as shown in figure 1.7.

Diagram not getting Copied

Fig 1.7 (a) Capacitors connected in series (b) Capacitors connected in parallel

If , and capacitors are connected in series as shown in figue 1.7 (a), the equivalent capacitance C is expressed by

$\frac1{\mathrm C}=\frac1{{\mathrm C}_1}+\frac1{{\mathrm C}_2}+...+\frac1{{\mathrm C}_{\mathrm n}}$ (24)

If two inductors C1 and C2 are connected in series, then the equivalent capacitance is expressed by

$\frac1{\mathrm C}=\frac1{{\mathrm C}_1}+\frac1{{\mathrm C}_2}$
$C=\frac{C_1C_2}{C_1+C_2}$ (25)

If C1, C2 and Cn inductors are connected in parallel as shown in figue 1.7 (b), the equivalent capacitance C is expressed by

$C=C_1+C_2+...+C_n$ (26)

Behaviour of Capacitor for AC and DC Sources:

Ideally, the capacitors behaves as an open circuit for the dc and behaves as a short circuit for ac. Generally, it allows ac and opposes dc. Figure 1.8 shows the behaviour of the capacitor at ideal condition.

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Fig 1.8 (a) Capacitor (b) capacitor behaves as an open circuit for dc (c) capacitor behaves as a short circuit for ac.

The current through a capacitor is represented in time domain by the equation (22). Similarly, in the frequency domain the current is represented by

$i=j\omega Cv$ (27)

From (27) $\frac vi=-JX_C$ and $X_C=\frac1{\omega C}=\frac1{2\pi fC}$ (28)

Where XC is the reactance of the capacitor measured in ohms and f is the frequency in Hz.

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