Electrical Elements

Capacitor Element

The constitutive equation is:

Since power is given by iu, by substituting Equation 2.13, the energy in a capacitor may be expressed as

This is the electrostatic energy of a capacitor.

Also,

Hence, for a capacitor,

U (0 ) =u (0- )

Unless an infinite current is applied to a capacitor. We summarize:

1.       Voltage is an appropriate response variable (or state variable) for a capacitor element.

2.       Voltage across a capacitor cannot change instantaneously unless an infinite current is applied.

3.       Voltage is a natural output variable and current is a natural input variable for a capacitor.

Inductor Element

The constitutive equation is

Energy

This is the electromagnetic energy of an inductor.

Also,

Hence, for an inductor,

i(0 )=i(0-)

Unless an infinite voltage is applied. We summarize:

1.       Current is an appropriate response variable (or state variable) for an inductor.

2.       Current through an inductor cannot change instantaneously unless an infinite voltage is applied.

3.       Current is a natural output variable and voltage is a natural input variable for an inductor.