FOCUS ON MATH
Integral VoltageCurrent Relationship
The capacitance
may be defined by the voltagecurrent relationship:
The ideal capacitor defined by the above
equation is a mathematical model of a real
device. The above equation provides several
important characteristics. A timeconstant
voltage across a capacitor results in zero
current passing through it; a capacitor
is therefore an open circuit to DC.
The capacitor voltage may be expressed in
terms of the current by integrating the
above equation
Now, we integrate the above Equation between
the times t_{0}
and t_{1}
and between the corresponding voltages v(
t_{0})
and v(
t_{1})
The above equation may
be written as an indefinite integral plus
a constant of integration
where the constant of integration
depends on the initial conditions (t
= 0). The power delivered to the capacitor
is
