BLM1612 Circuit Theory
Lecture 7
Capacitors & Inductors
Capacitance
A capacitor is a passive linear circuit element which stores energy in the
electric field in the space between two conducting bodies occupied by a
material with permittivity .
dv
i = C
dt
charged by applying current (for a finite amount of time, from another source) to
its terminals
discharged when it provides current (for a finite amount of time, to a circuit)
from its terminals
Capacitor Current & Voltage
Capacitor Characteristics
Example 7.1

Determine the current i flowing through the capacitor for
the two voltage waveforms of Fig. 7.3 if C 2 F.

Answer:
Example 7.2

Find the capacitor voltage that is associated with the current shown
graphically. The value of the capacitance is 5 µF.

Answer:
Capacitor Energy Storage
Example (page 223, #7.3)
Find the maximum energy stored in the capacitor of Figure and
the energy dissipated in the resistor over the interval 0 < t < 0.5 s.
Example (page 223, #7.3)
Plot the current through the
resistor, capacitor, and voltage
source between 0 < t < 0.5 s.
Inductance
An inductor is another passive linear circuit element which stores
energy in the magnetic field in the space between current-carrying
wires occupied by a material with permeability .
Inductor Current & Voltage
Example 7.4

Given the waveform of the current in a 3 H inductor as
shown in Figure, determine the inductor voltage and
sketch it.

Answer:
Example 7.5

Find the inductor voltage that results from applying the current
waveform shown in Figure to the inductor of Example 7.4.

Answer:
Inductor Characteristics
Example 7.6
  The
voltage across a 2 H inductor is known to be
6 cos 5t V. Determine the resulting inductor
current if i(t=-π/2) =1A.
Inductor Energy Storage
Example 7.7

Find the maximum energy stored in the inductor of Fig.
7.16, and calculate how much energy is dissipated in the
resistor in the time during which the energy is being
stored in, and then recovered from, the inductor.
Example (page 232, #7.7)
Applications: Resistors
Applications: Op Amps
Applications: Capacitors / Inductors
DC Capacitor Circuits
DC Inductor Circuits
Equivalent Series Inductance
Equivalent Parallel Inductance
Example (page 254, #32, modified)
Equivalent Parallel Capacitance
Equivalent Series Capacitance
Example 7.8
  Simplify
the network of Figure using seriesparallel combinations.
  Answer:
Consequences of Linearity
  use
of Kirchhoff’s laws in RLC circuits
  it will be possible to define a voltage-current ratio
(called impedance) or a current-voltage ratio
(called admittance)
  Thévenin’s and Norton’s theorems are based on
the linearity of the initial circuit, the applicability of
Kirchhoff’s laws, and the superposition principle.
The general RLC circuit conforms perfectly to
these requirements
Example 7.9
  Write
appropriate nodal equations for the circuit
  Answer:
Simple Op Amp Circuits with Capacitors
Example 7.10
  Derive
an expression for the output voltage of the
op amp circuit
Example (page 237, #7.8, modified)
Capacitors & Inductors + Op Amps
Chapter 7 Summary & Review