Capacitors
solution
*note* theres no current flowing through the 5Kohm resistor because it is connected to an open circuit (i.e i = 0), so this means that the 2Kohm and 4kohm resistors are in series. *note* the voltage is obtained by using the resistor that's in parallel with the capacitor
start of *INDUCTORS*
*passive* element designed to store energy in its *magnetic* field
Michael Faraday
- discovered electromagnetic induction (breakthrough for engineers because it provided a way of generating electricity) -
linear inductor
- its inductance is *independent* of the current. i.e. V = L(di/dt)
1 farad =
1 coulomb/volt
_____ capacitors produce very high capacitance
electrolytic
when is the capacitor discharging in terms of v and i
when V * i < 0
when is the capacitor being charged, in terms of v and i
when V < 0 and i <0 or when V >0 and i >0
Ceq of capacitance in series
when a voltage source is applied
when does v = 0 through an inductor
when current is constant
*A capacitor is an open circuit to dc* is derived from which property of a capacitor
when voltage isn't changing current is equal to 0
equation to find capacitance (not dependent on voltage or charge is
where: A = surface area of each plate d = distance between the plates E = permittivity of the dielectric material *only applied to parallel plates*
how to make an ideal integrator for an inverter op amp?
you replace rf with a capacitor
common types of variable capacitors
- trimmer - filmtrim
so for a capacitor with constant voltage, i = ?
0
in general, 3 factors determine the value of capacitance
1) surface area of plates 2) spacing between the plates 3) permittivity of the material
important properties of an inductor are:
1) voltage across an inductor is 0 when the current is constant 2) the current through an inductor cannot change instantaneously (opposition to change in current flowing) 3) *ideal* inductor does not dissipate energy. 4) practical, *nonideal* inductor has a significant resistive component.
important properties of capacitors
1) when voltage across a capacitor is not changing, *i=0.* 2) voltage on a capacitor must be *continuous* 3) ideal capacitor *does not dissipate energy.* 4) a real *nonideal* capacitor has a parallel model *leakage resistance.*
*AN IDEAL CAPACITOR CANNOT DISSIPATE ENERGY* so energy between the plates can be retrieved
:P
equivalent capacitor Ceq of N capacitors in parallel
Ceq = C1 + C2 + ... Cn it's the sum of the individual capacitance *note* this is with a current source applied
capacitors are used to block ____, pass ___, shift phase, store ___, start motors, and supress _____
dc, ac, energy, noise
how does length of coil affect inductance
decreasing the length of the coil, will increase the inductance
the amount of charge stored, represented by q, when a voltage source is applied to a capacitor, is (directly/ inversely) proportional to the applied voltage v.
directly
if current is allowed to pass through an inductor, it is found that the voltage across the inductor is....
directly proportional to the time rate of change of the current where L is the constant of proportionality called the *inductance*
electromagnetic induction
discovery by Michael faraday which was a breakthrough for engineers because it provided a way of generating electricity paved the way for electric motor and generator to operate on
(T/F) Inductors have very high resistance
false because inductors have a lot of conducting wire, their resistance is *small*
(T/F) Capacitance depends on Voltage and q charge on capacitor plates
false; it doesn't depend on either. IT depends on the physical dimensions of the capacitor
*example:* The voltage across a 5- uF capacitor is: v(t) = 10cos(6000t)V
have to take the derivative of
how does permeability affect inductance
higher permeability in the core, increases inductance
how does cross sectional area affect inductance
increasing the cross sectional area, increases inductanec
how does the number of turns around a cylinder affect inductance
increasing the number of coils, increases inductance
L
inductance (constant of proportionality) units: Henry(H)
how do you enhance the inductive effect
inductor is formed into a cylindrical coil with many turns of conducting wire
how To solve simple differential equations using the analog computer
integrator circuits, summing amplifiers, and inverting/noninverting amplifiers for negative/positive scaling.
what is the relationship between capacitor voltage rating and capacitance?
inversely related
capacitance
is the ratio of the charge on one plate of a capacitor to the voltage difference between the two plates, measured in farads (F). *AKA* the amount of charge stored per plate for a unit voltage difference in a capacitor
if an ideal capacitor does not dissipate energy then what does it do ?
it takes energy from the circuit and stores it in between the plates (electric field) and returns previously stored energy when delivering power to the circuit
trimmer (padder) capacitor
its capacitance is often placed in parallel with another capacitor so that the equivalent capacitance can be varied slightly
inductance of an inductor depends on what ? what's the formula?
its physical dimension and construction i.e. N, number of turns L, its length A, cross sectional area u, permeability of the core
parallel model leakage resistance in an nonideal capacitor
leakage resistance can be as high as 100 Mohms and can be neglected for most practical applications.
polyester
light in weight, stable and their change with temperature is predictable
voltage- current relation of a capacitor equation
obtained by integrating both sides of: i = V(dv/dt) v(t0) = q(t0) / C
integrator
op amp circuit whose output is proportional to the integral of the input signal
differentiator
op amp circuit whose output is proportional to the rate of change of the input signal
common types of fixed value capacitors include
polyester ceramic electrolytic
inductance
property whereby an inductor resists change in current through it. it's measured in henrys
formula for finding the charge stored by capacitor is
q = CV where C is the constant of proportionality (i.e. the *capacitance* of the capacitor)
how to create a differentiator from an op amp
replace the input resistor with a capacitor
voltage source connected to a capacitor
source deposits a positive charge q on one plate and a negative charge -q on the other. & *the capacitor stores the electric charge*
the core of an inductor can be made of
steel, air, plastic, or iron
how do we obtain the current- voltage relationship of the capacitor?
take the derivative of both sides of the previous equation, differentiating both sides gives
*An inductor acts like a short circuit to dc* is derived from what
the fact that when current is constant through an inductor, the voltage is 0
how does the permittivity of the material affect capacitance?
the greater the permittivity of the material, the greater the capacitance.
how does surface area of plates affect capacitance?
the large the surface area, the greater the capacitance
how does spacing between the plates affect capacitance
the smaller the space, the greater the capacitance
(T/F) Capacitor voltage depends on the past history of the capacitor current
true
(T/F) any conductor of electric current has inductive properties and may be regarded as an inductor
true
(T/F) if a battery (dc voltage) is connected across a capacitor, the capacitor charges
true
(T/F) two capacitors in series is the same as two resistors in series
true
(T/F) The current through a capacitor can change instantaneously
true, voltage cannot
(T/F) the voltage through an inductor can change abruptly
true; the current cant
capacitor
two conducting plates separated by an insulator (or dielectric) ex: plates of aluminum foil and insulator/dielectric air, ceramic, paper or mica
___ capacitors are used in radio receivers allowing one to tune to various stations
variable
for a capacitor to carry current, its voltage must
vary with time
*The voltage on a capacitor cannot change abruptly* is derived from which property of a capacitor
voltage on the capacitor must be *continuous*