Jest Joyce C. Tagalogon BSECE-2 (Chapter 7 Summary of Learnings)
Capacitor
A two terminal device that is consist of two
conducting elements with a presence of
insulator or dielectric in between. Due to the
presence of the insulator transferring of
chargers between the conducting elements is
not possible not unless done by the external
circuitry connected to
its terminals.
Based on the diagram
the transferring of
charges from one
plate to the other requires the unlike charges to
be separated (positive charge moving up
leaving negative charge at the bottom) thus
work is performed, raising the potential. Thus,
the charge is directly proportional to the
potential deference of two plates. If voltage
came in contact with charge in the capacitor the
capacitor will be charged therefore voltage is
also directly proportional to charge that could be
written as
q=Cv q- charge
C- capacitance (unit is farad F=c/v)
v-voltage
differentiating current we will
have
the
current-voltage
relation for a capacitor.
Change in voltage’s polarity or
current direction will lead to a
-i
INDUCTORS
A two-terminal device that
consists of a coiled conducting
wire. Works the same as the
capacitor.
This law states that the voltage is
equal to the time
rate of change of
the total magnetic flux. Yields,
The unit for inductance L is Henry H=Wb/A,
V.s/A
Integrating from time t0 to t
and solving for i(t)
an inductor acts like a short circuit if i is
constant and
the voltage v is
zero.
ENERGY STORAGE IN INDUCTORS
It temporarily stores energy in a form of
magnetic field
SERIES AND PARALLEL INDUCTORS
integrating both sides of
time to and t.
between
where v(to) = q(t0)/C is the voltage on C at time
to.
ENERCY STORACE IN CAPACITORS
Capacitors temporarily stores energy in a form
of electrostatic field.
The circuit is in a DC STEADY STATE if ALL
current through and voltage across each
element’s ae constant. Capacitors are like open
circuits (their currents are zero) and inductors
are like short circuits (their voltages are zero).
SWITCHES
open prior to t=0
SERIES AND PARALLEL CAPACITORS
close prior to t=0
Jest Joyce C. Tagalogon BSECE-2 (Chapter 8 Summary of Learnings)
SOURCE-FREE RC CIRCUIT
THE GENERAL CASE
A circuit that has resistor and capacitor in series
The equations describing the networks of the
where the circuit response is provided by the
previous sections are all special cases of a
energy initially stored in
general expression given by
the capacitor.
Energy
in
initially
stored in a capacitor is
where y is the unknown variable, such as v or i,
defined as
and P and Q are constants.
The equation for the RC circuit is
Natural response or source-free response is
characterized as the response of a circuit
element and not by the external voltage or
current source.
TIME CONSTANTS
The time required for the natural response to
decay by a factor of i/e is dependent to RC
which is the time constant written as
The unit of tau
The v equation for the RC circuit in terms of time
constant is
SOURCE-FREE RL CIRCUIT
A circuit consist of
resistor and inductor in
series connection where
the circuit response is
provided by the energy
initially stored in the inductor.
The stored energy at t=0 is written as
The equation for the RL circuit is
Just like the RC circuit it has a time
constant written as
Thus, the equation for the RL circuit in terms of
tau is
RESPONSE TO A CONSTANT FORCING
FUNCTION
The general solution for the circuit that is consist
of one resistor, one capacitor and at least one
constant independent source is the solution for
solving for a complete response.
Forcing function are constant independent
voltage or current sources that drives a circuit
along with the initial stored energies.
Forced response is when a component is due
entirely to the forcing function.
Complete response= natural response + forced
response
A SHORTCUT PROCEDURE
This technique involves formulating the solution
by merely inspecting the circuit which is very
helpful in finding the currents and voltages in
circuits with dc sources.
THE UNIT STEP FUNCTION
It is the function equal to zero for all negative
values of its argument and equal to I for all
positive values of its argument which may be
used to represent voltages or currents with finite
discontinuities.Step function is denoted as
Mathematicaly described as
singularity functions are
forcing functions with changed values
THE STEP RESPONSE
It is the response to a unit step input with no
initial energy stored in the circuit. all the currents
and voltages in the network are zero as t = 0due to the fact that the step function and is zero
for
APPLICATION OF SUPERPOSITION
we consider the use of superposition for
obtaining solutions of RC and RL circuits
containing two or more independent sources.
Jest Joyce C. Tagalogon BSECE-2 (Chapter 8 Summary of Learnings)
SECOND ORDER CIRCUITS
A second order circuit is a circuit either a series
or parallel that contains a resistor and 2-energy
storing devices could be capacitor or inductor or
both. This is due to the fact that the sum of all
voltages around the loops results to a second
order differential equation.
The formulas usually applied are
The process of solving the circuits need to be
systematic in order for the circuit to be solved
easier.
The key in solving the second order circuit
The first thing we need to do is express what
we need to solve for.
We need to find the values of the current
through the inductor and the voltage across the
capacitor prior to t=0.
We need to repeat the same process but
considering the values right after t=0.
These values right before and right after should
be the same as the voltage across the
capacitor and the current through the inductor
is not instantaneous
Thus,
The next process would be with switch closed
solve for the change of current inside the
inductor with respect to time and the change of
the voltage inside the capacitor with respect to
time.
At a steady state solve for the current through
the inductor and voltage across the capacitor
as t approaches infinity