PRACTICAL MATLAB® FOR ENGINEERS PRACTICAL MATLAB

130 Practical MATLAB® Applications for Engineers

where τ = RC, and

it

vt

R

V

R

() C ett

() /

^0  for 0

R.2.101 When a circuit switches from one set of conditions to a new set of conditions,
there is a transition period where voltages and currents are adjusting to the new
conditions. The term transient response is the adjusting transition time from its
initial to its fi nal voltage and current values. The transition takes place in the
interval 0 ≤ t ≤ 5 τ; and the steady-state response refers to the voltages and cur-
rents for t > 5 τ.

R.2.102 Let us now review and summarize the inductor’s characteristics.

There is no voltage drop across an inductor if the current through it is not chang-

ing with time. An inductor is, therefore, a short circuit for DC, and vL(t) = 0, for

t > 5 τ.

A fi nite amount of energy can be stored in an inductor even if the voltage across

the inductor is zero.

An inductor resists abrupt changes in current.

An inductor never dissipates energy; it is only capable of storing energy. This

statement is true for the ideal inductor; however, it is false for the real inductor,

which always possesses some internal resistance.

R.2.103 The capacitor’s characteristics are summarized as follows:

The current through the capacitor is zero, if the voltage across it is not changing

with time (DC).

A fi nite amount of energy can be stored in a capacitor even if the current through

the capacitor is zero.

A capacitor resists abrupt change in voltage across it.

A pure capacitor cannot dissipate energy; it can only store energy.

R.2.104 For example, analyze the circuit shown in Figure 2.30, and write the differential
equation for t ≥ 0, if the switch opens at t = 0 after being closed for a long time.
Obtain expressions for vC(t) and iR(t) for t > 0.

• • • • • • • •

C R

+

−

vC(0) =V 0

v(t)

FIGURE 2.29
Charged capacitor in an RC series circuit.