Capacitors
What are Capacitors?
- In a way, a capacitor is a little like a battery. Although
they work in completely different ways, capacitors and batteries both store
electrical energy. If you have read know how batteries work, then you know that a battery has two terminals. Inside the battery,
chemical reactions produce electrons on
one terminal and absorb electrons on the other terminal. A capacitor is much
simpler than a battery, as it can't produce new electrons -- it only stores
them.
In this section, we'll learn exactly what a capacitor is,
what it does and how it's used in electronics. We'll also look
at the history of the capacitor and how several people helped shape its
progress.
Inside the capacitor, the terminals connect to two metal plates
separated by a non-conducting substance, or dielectric.
In theory, the dielectric can be any non-conductive
substance. However, for practical applications, specific materials are used
that best suit the capacitor's function. Mica, ceramic, cellulose, porcelain,
Mylar, Teflon and even air are some of
the non-conductive materials used. The dielectric dictates what kind of
capacitor it is and for what it is best suited. Depending on the size and type
of dielectric, some capacitors are better for high frequency uses, while some
are better for high voltage applications. Capacitors can be manufactured to
serve any purpose, from the smallest plastic capacitor in your calculator, to
an ultra capacitor that can power a commuter bus. NASA uses glass
capacitors to help wake up the space shuttle's circuitry and help deploy space
probes.
Capacitor Circuit
In an electronic circuit, a capacitor is shown
like this:
When you connect a capacitor to a battery,
here's what happens:
- The
plate on the capacitor that attaches to the negative terminal of the
battery accepts electrons that
the battery is producing.
- The
plate on the capacitor that attaches to the positive terminal of the
battery loses electrons to the battery.
Once it's charged, the capacitor has the same voltage as
the battery (1.5 volts on the battery means 1.5 volts on the capacitor). For a
small capacitor, the capacity is small. But large capacitors can hold quite a
bit of charge. You can find capacitors as big as soda cans that hold enough
charge to light a flashlight
bulb for a minute or more.
Let's say you hook up a capacitor like this:
Here you have a battery, a light bulb and a
capacitor. If the capacitor is pretty big, what you will notice is that, when
you connect the battery, the light bulb will light up as current flows from the battery to
the capacitor to charge it up. The bulb will get progressively dimmer and
finally go out once the capacitor reaches its capacity. If you then remove the
battery and replace it with a wire, current will flow from one plate of the
capacitor to the other. The bulb will light initially and then dim as the
capacitor discharges, until it is completely out.
Capacitors in Series Connection:
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To calculate the total overall capacitance of two capacitors
connected in this way you can use the following formula:
1/CTotal = 1/C1
+ 1/C2 + 1/Cn ….
Example: To calculate the total capacitance for these two
capacitors in series.
Capacitors in Parallel Connection:
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To calculate the total overall capacitance of two
capacitors connected in this way you can use the following formula:
CTotal = C1 + C2 + Cn
…..
Example: Calculate the total capacitance of these capacitors in parallel.
CTotal = C1 + C2 + C3
= 0.1uF + 0.2uF + 0.3uF
= 0.6uF
Voltage - Current relationship of a capacitor
There is a relationship between the
charge on a capacitor and the voltage across the capacitor. The
relationship is simple. For most dielectric/insulating materials, charge and
voltage are linearly related.
Q = C V
where:
- V is
the voltage across the plates.
You will need to define a polarity for that voltage. We've
defined the voltage above. You could reverse the "+" and
"-".
- Q is
the charge on the plate with the "+" on the voltage
polarity definition.
- C is a
constant - the capacitance of the capacitor.
The relationship
between the charge on a capacitor and the voltage across the capacitor is
linear with a constant, C, called the capacitance.
Q = C V
When V is
measured in volts, and Q is measured in coulombs, then C has the units of farads.
Farads are really coulombs/volt.
Because dq(t)/dt is the current through the
capacitor, you get the following i-v relationship:
To express the voltage across the capacitor in terms of the
current, you integrate the preceding equation as follows:
The second term in this equation is the initial voltage
across the capacitor at time t = 0.
Energy stored in a capacitor
The energy stored on a capacitor can
be calculated from the equivalent expressions:
Inductors
What are Inductors?
-An inductor, also called a coil or reactor,
is a passive two-terminal electrical component which resists
changes in electric current passing through it. It consists of
a conductor such as a wire, usually wound into a coil. When a current flows
through it, energy is
stored temporarily in a magnetic
field in the coil. When the current flowing through an inductor
changes, the time-varying magnetic field induces a voltage in
the conductor, according to Faraday’s law of electromagnetic induction,
which opposes the change in current that created it.
An inductor is characterized by its inductance,
the ratio of the voltage to the rate of change of current, which has units of henries (H).
Inductors have values that typically range from 1 µH (10−6H) to 1 H.
Many inductors have a magnetic core made of iron or ferrite inside
the coil, which serves to increase the magnetic field and thus the inductance.
Along with capacitors and resistors,
inductors are one of the three passive linear circuit
elements that make up electric circuits. Inductors are widely used in alternating current (AC) electronic
equipment, particularly in radio equipment. They are used to block the flow of AC
current while allowing DC to pass; inductors designed for this purpose are
called chokes. They are also used in electronic
filters to separate signals of different frequencies,
and in combination with capacitors to make tuned
circuits, used to tune radio and TV receivers.
Inductors in Series Connection
Thus, the total inductance for series inductors is more than
any one of the individual inductors' inductances. The formula for calculating
the series total inductance is the same form as for calculating series
resistances:
Inductors in Parallel Connection
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Thus, the total inductance is less than any one of the
individual inductors' inductances. The formula for calculating the parallel
total inductance is the same form as for calculating parallel resistances:
Voltage - Current relationship of an inductor
Here’s the defining equation for the inductor:
where the inductance L is a constant
measured in henries (H). Here is the same equation in
graphical form.
To express the current through the inductor in terms of the
voltage, you integrate the preceding equation as follows:
Energy stored in an Inductor
The energy equation implies that the energy in the inductor
is always positive. The inductor absorbs power from a circuit when storing
energy, and the inductor releases the stored energy when delivering energy to
the circuit.
Reflection
This week, we also discussed Capacitors and Inductors together with Maximum Power Transfer. Capacitors and Inductors are passive elements in a circuit, meaning that they cannot generate energy, they drop it instead. Capacitors are components that store electrical energy and when the capacitor is full of electrical energy, it is in a "charged" state. To discharge a capacitor, you need to connect a resistor in both of its terminals. Capacitors are made up of two metal plates and separated by a non-conducting substance or dielectric. Capacitors are also measured in farads but most of the time, You'll only find capacitors in micro farads (F) because one farad is a pretty huge number. Inductors are basically just coils of conducting wires and they are measured in henries (H). Like the capacitor, it also stores electrical energy but it stores it in a form of a magnetic field.
Video(s):
Capacitors
Inductors
Reflection
This week, we also discussed Capacitors and Inductors together with Maximum Power Transfer. Capacitors and Inductors are passive elements in a circuit, meaning that they cannot generate energy, they drop it instead. Capacitors are components that store electrical energy and when the capacitor is full of electrical energy, it is in a "charged" state. To discharge a capacitor, you need to connect a resistor in both of its terminals. Capacitors are made up of two metal plates and separated by a non-conducting substance or dielectric. Capacitors are also measured in farads but most of the time, You'll only find capacitors in micro farads (F) because one farad is a pretty huge number. Inductors are basically just coils of conducting wires and they are measured in henries (H). Like the capacitor, it also stores electrical energy but it stores it in a form of a magnetic field.
Video(s):
Capacitors
“I've found out so much about electricity that I've reached
the point where I understand nothing and can explain nothing.
[Describing his experiments with the Leyden jar.]”
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