electrical circuits
DESCRIPTION
ELECTRICAL CIRCUITS. The CELL. The cell stores chemical energy and transfers it to electrical energy when a circuit is connected. When two or more cells are connected together we call this a Battery. The cells chemical energy is used up pushing a current round a circuit. - PowerPoint PPT PresentationTRANSCRIPT
ELECTRICAL ELECTRICAL CIRCUITSCIRCUITSELECTRICAL ELECTRICAL CIRCUITSCIRCUITS
The CELLThe CELLThe CELLThe CELL
The cell stores chemical energy and transfers
it to electrical energy when a circuit is
connected. When two or more cells are
connected together we call
this a Battery.
The cells chemical energy is
used up pushing a current
round a circuit.
What is an electric current?
An electric current is a flow of microscopic
particles called electrons flowing through
wires and components.
+-
In which direction does the current flow? from the Negative terminal to the Positive terminal of a cell.
simple circuitssimple circuits
Here is a simple electric circuit. It has a cell, a
lamp and a switch.
To make the circuit, these components are
connected together with metal connecting wires.
cell
lamp
switch
wires
simple circuitssimple circuitsWhen the switch is closed, the lamp lights up. This is because there is a continuous path of metal for the electric current to flow around.
If there were any breaks in the circuit, the current could not flow.
circuit diagramcircuit diagram
cell switch
lamp
wires
Scientists usually draw electric circuits using symbols;
circuit diagramscircuit diagramsIn circuit diagrams components are represented by the following symbols;
cell battery
switch
lamp
motorammeter
voltmeter
buzzer
resistor
variable resistor
types of circuittypes of circuit
There are two types of electrical circuits;
SERIES CIRCUITS PARALLEL CIRCUITS
The components are connected end-to-end, one after the other.
They make a simple loop for the current to flow round.
SERIES CIRCUITS
If one bulb ‘blows’ it breaks the whole circuit and all the bulbs go out.
PARALLEL CIRCUITS
The current has a choice of routes.
The components are connected side by side.
If one bulb ‘blows’ there is still be a complete circuit to the other bulb so it stays alight.
measuring current
Electric current is measured in amps (A)
using an ammeter connected in series in
the circuit.
A
measuring current
A A
This is how we draw an ammeter in a circuit.
SERIES CIRCUIT PARALLEL CIRCUIT
measuring currentSERIES CIRCUIT
PARALLEL CIRCUIT
• current is the same
at all points in the
circuit.
2A 2A
2A
• current is shared between the components
2A2A
1A
1A
copy the following circuits and fill in the missing ammeter readings.
?
?
4A
4A
4A
3A?
?
1A
?
3A
1A
1A
measuring voltage
The ‘electrical push’ which the cell gives to the
current is called the voltage. It is measured in
volts (V) on a voltmeter
V
Different cells produce different voltages. The
bigger the voltage supplied by the cell, the bigger
the current.
measuring voltage
Unlike an ammeter a voltmeter is connected
across the components
Scientist usually use the term Potential
Difference (pd) when they talk about voltage.
measuring voltage
V
This is how we draw a voltmeter in a circuit.
SERIES CIRCUIT PARALLEL CIRCUIT
V
V
measuring voltage
VV
V
series circuit
1.5V
• voltage is shared between the components
1.5V
3V
• voltage is the same in all parts of the circuit.
3V
parallel circuit
3V
3V
measuring current & voltage
copy the following circuits on the next two slides.
complete the missing current and voltage readings.
remember the rules for current and voltage in series and parallel circuits.
measuring current & voltage
V V
6V4A
A
A
a)a)
measuring current & voltage
V
V
6V4A A
A
A
b)b)
answers
3V 3V
6V
4A 4A6V
6V
6V4A 4A
2A
2A
4A
a)a) b)b)
Electric CircuitsIn electricity, the concept of voltage will be like
pressure. Water flows from high pressure to low pressure (this is consistent with our previous analogy that Voltage is like height since P = gh for fluids) ; electricity flows from high voltage to low voltage.
But what flows in electricity? Charges!
How do we measure this flow? By Current:
current = I = q / t
UNITS: Amp(ere) = Coulomb / second
The rate at which electrons move along field lines is called drift speed, typically about 10-4 m/s
Electric current defined in terms of the flow of positive charge opposite the electrons is called conventional currentCurrent will always be in the same direction as the local electric field
Voltage Sources:batteries and power supplies
A battery or power supply supplies voltage. This is analogous to what a pump does in a water system.
Question: Does a water pump supply water? If you bought a water pump, and then plugged it in (without any other connections), would water come out of the pump?
Question: Does the battery or power supply actually supply the charges that will flow through the circuit?
• Charges move from higher to lower potential
• For the process to continue, charges that have moved from a higher to lower potential must be raised back to a higher potential again
• A battery is able to add charges and raise the charges to higher electric potential
Symbol for a battery
Voltage Sources:batteries and power supplies
Just like a water pump only pushes water (gives energy to the water by raising the pressure of the water), so the voltage source only pushes the charges (gives energy to the charges by raising the voltage of the charges).
Just like a pump needs water coming into it in order to pump water out, so the voltage source needs charges coming into it (into the negative terminal) in order to “pump” them out (of the positive terminal).
Voltage Sources:batteries and power supplies
Because of the “pumping” nature of voltage sources, we need to have a complete circuit before we have a current.
Circuit Elements
In this first part of the course we will consider two of the common circuit elements:
capacitor
resistor
The capacitor is an element that stores charge for use later (like a water tower).
The resistor is an element that “resists” the flow of electricity.
Electrical Resistance &
Ohms’ Law
The current established is directly proportional to the voltage difference
Ohm’s Law: ΔV I∝
In a plot of ΔV vs I,
the slope is called the electrical resistance
Resistance
Current is somewhat like fluid flow. Recall that it took a pressure difference to make the fluid flow due to the viscosity of the fluid and the size (area and length) of the pipe. So to in electricity, it takes a voltage difference to make electric current flow due to the resistance in the circuit.
ResistanceBy experiment we find that if we increase the
voltage, we increase the current: V is proportional to I. The constant of proportionality we call the resistance, R:
V = I*R Ohm’s Law
UNITS: R = V/I so Ohm = Volt / Amp.
The symbol for resistance is
ResistanceJust as with fluid flow, the amount of resistance does
not depend on the voltage (pressure) or the current (volume flow). The formula V=IR relates voltage to current. If you double the voltage, you will double the current, not change the resistance. The same applied to capacitance: the capacitance did not depend on the charge and voltage - the capacitance related the two.
As was the case in fluid flow and capacitance, the amount of resistance depends on the materials and shapes of the wires.
Resistance
The resistance depends on material and geometry (shape). For a wire, we have:
R = L / A
where is called the resistivity (in Ohm-m) and measures how hard it is for current to flow through the material, L is the length of the wire, and A is the cross-sectional area of the wire. The second lab experiment deals with Ohm’s Law and the above equation.
Electrical Power
The electrical potential energy of a charge is:
U = q*V .
Power is the change in energy with respect to time: Power = U / t .
Putting these two concepts together we have:
Power = (qV) / t = V(q) / t = I*V.
Electrical Power
Besides this basic equation for power:
P = I*V
remember we also have Ohm’s Law:
V = I*R .
Thus we can write the following equations for power: P = I2*R = V2/R = I*V .
To see which one gives the most insight, we need to understand what is being held constant.
Example
When using batteries, the battery keeps the voltage constant. Each D cell battery supplies 1.5 volts, so four D cell batteries in series (one after the other) will supply a constant 6 volts.
When used with four D cell batteries, a light bulb is designed to use 5 Watts of power. What is the resistance of the light bulb?
Example
We know V = 6 volts, and P = 5 Watts; we’re looking for R.
We have two equations:
P = I*V and V = I*R
which together have 4 quantities:
P, I, V & R..
We know two of these (P & V), so we should be able to solve for the other two.
Example
Using the power equation we can solve for I:
P = I*V, so 5 Watts = I * (6 volts), or
I = 5 Watts / 6 volts = 0.833 amps.
Now we can use Ohm’s Law to solve for R:
V = I*R, so
R = V/I = 6 volts / 0.833 amps = 7.2 .
Example extended
If we wanted a higher power light bulb, should we have a bigger resistance or a smaller resistance for the light bulb?
We have two relations for power that involve resistance:
P=I*V; V=I*R; eliminating V gives: P = I2*R and
P=I*V; I=V/R; eliminating I gives: P = V2 / R .In the first case, Power goes up as R goes up; in the
second case, Power goes down as R goes up.Which one do we use to answer the above question?
Example extended
Answer: In this case, the voltage is being held constant due to the nature of the batteries. This means that the current will change as we change the resistance. Thus, the P = V2 / R would be the most straight-forward equation to use. This means that as R goes down, P goes up. (If we had used the P = I2*R formula, as R goes up, I would decrease – so it would not be clear what happened to power.)
The answer: for more power, lower the resistance. This will allow more current to flow at the same voltage, and hence allow more power!
Kirchhoff’s Laws
• Junction Law: at a junction in a circuit, the sum of the current entering the junction will equal the sum of the current leaving.
Σ I = Σ I in out
• Loop Law: the sum of the potential drops around any closed loop must add to
Σ V = 0 loop
Connecting Resistors
There are two basic ways of connecting two resistors: series and parallel.
In series, we connect resistors together like railroad cars; this is just like we have for capacitors:
+ - + -
high V low V
R1 R2
Formula for Series:
To see how resistors combine to give an effective resistance when in series, we can look either at
V = I*R,
or at
R = L/A .Vbat
R1
R2+
-
I
V1 V2
Formula for SeriesUsing V = I*R, we see that in series the current must
move through both resistors. (Think of water flowing down two water falls in series.) Thus
Itotal = I1 = I2 .Also, the voltage drop across the two resistors add to
give the total voltage drop:(The total height that the water fell is the addition of the two heights of
the falls.)
Vtotal = (V1 + V2). Thus, Reff = Vtotal / Itotal =
(V1 + V2)/Itotal = V1/I1 + V2/I2 = R1 + R2.
Formula for Series
Using R = L/A , we see that we have to go over both lengths, so the lengths should add. The distances are in the numerator, and so the values should add.
This is just like in R = V/I (from V = IR) where the V’s add and are in the numerator!
Note: this is the opposite of capacitors when connected in series! Recall that
C = Q/V, where V is in the denominator!
Formula for Parallel ResistorsThe result for the effective resistance for a
parallel connection is different, but we can start from the same two places:
(Think of water in a river that splits with some water flowing over one fall and the rest falling over the other but all the water ending up joining back together again.) V=I*R, or R = L/A .
+
-
Vbat R1 R2
Itotal
I1 I2
Formula for Parallel Resistors
V=I*R, or R = L/A
For parallel, both resistors are across the same voltage, so Vtotal = V1 = V2 . The current can go through either resistor, so: Itotal = (I1 + I2 ) .
Since the I’s are in the denominator, we have:
R = Vtotal/Itotal = Vtotal/(I1+I2); or
1/Reff = (I1+I2)/Vtotal = I1/V1 + I2/V2 = 1/R1 + 1/R2.
Formula for Parallel Resistors
If we start from R = L/A , we can see that parallel resistors are equivalent to one resistor with more Area. But A is in the denominator (just like I was in the previous slide), so we need to add the inverses:
1/Reff = 1/R1 + 1/R2 .
Terminal VoltageTerminal voltage, VT , is the potential difference
between the terminals of a battery.
Ideal voltage, VB , is determined by the chemistry of the battery.
Internal resistance, ir : some charge will be los due to the random thermal motion of the battery
Terminal voltage will be: VT = VB - ir
For recharging a battery: VT = VB + ir
Current DivisionWhen current enters a junction, Kirchhoff’s first
law tells you the sum of the current entering must equal the sum of the current leaving.
Example: 8 = I + 4I + 5I I = 0.8 A
1/RP = 1/20 +1/5 +1/4 = ½ RP = 2Ω
V = IRP = 8 • 2 = 16V
16 = I1(20) I1 = 0.8A16 = I2(5) I2 = 3.2A16 = I3(4) I3 = 4A
Simple Circuits
• A simple circuit is a connection of batteries and resistors that meets 2 criteria
1. All batteries are in series
2. The equivalent resistance of the entire circuit can be obtained by repeated use of just the series and parallel equivalent resistance formulas
VB = 60 – 18 = 42V
1/RP = 1/12 + 1/6 = ¼ RP = 4Ω
Requiv = 4 + 8 + 6 + 3 = 21Ω
42 – I(21) = 0 I = 2A
VT60 = 60 – 2 • 1 = 58V
VT18 = 18 – 2 • 2 = 22V
2 = I + 2I I = 0.67A
Capacitance
We define capacitance as the amount of charge stored per volt: C = Qstored / V.
UNITS: Farad = Coulomb / Volt
Just as the capacity of a water tower depends on the size and shape, so the capacitance of a capacitor depends on its size and shape. Just as a big water tower can contain more water per foot (or per unit pressure), so a big capacitor can store more charge per volt.
Parallel Plate Capacitor
For a parallel plate capacitor, we can pull charge from one plate (leaving a Q on that plate) and deposit it on the other plate (leaving a +Q on that plate). Because of the charge separation, we have a voltage difference between the plates, V. The harder we pull (the more voltage across the two plates), the more charge we pull: C = Q /V. Note that C is NOT CHANGED by either Q or V; C relates Q and V!
Capacitance• What happens when a water tower is over-filled?
It can break due to the pressure of the water pushing on the walls.
• What happens when an electric capacitor is “over-filled” or equivalently a higher voltage is placed across the capacitor than the listed maximum voltage? It will “break” by having the charge “escape”. This escaping charge is like lightning - a spark that usually destroys the capacitor.
V or V ?
When we deal with height, h, we usually refer to the change in height, h, between the base and the top. Sometimes we do refer to the height as measured from some reference point. It is usually clear from the context whether h refers to an actual h or a h.
With voltage, the same thing applies. We often just use V to really mean V. You should be able to determine whether we really mean V or V when we say V.
Parallel Plate Capacitor
For this parallel plate capacitor, the capacitance is related to charge and voltage (C = Q/V), but the actual capacitance depends on the size and shape:
C plate A / d∝
A is the area of each plate, d is the distance between the plates
Energy Storage
If a capacitor stores charge and carries voltage, it also stores the energy it took to separate the charge. The formula for this is:
Estored = (1/2)QV = (1/2)CV2 ,
where in the second equation we have used the relation: C = Q/V .
Energy Storage
Note that previously we had:
U = q*V ,
and now for a capacitor we have:
Ucap = ½ QV = ½ CV2 = ½ Q2/C
Energy StorageThe reason is that in charging a capacitor, the
first bit of charge is transferred while there is very little voltage on the capacitor (recall that the charge separation creates the voltage!). Only the last bit of charge is moved across the full voltage. Thus, on average, the full charge moves across only half the voltage!
Hooking Capacitors Together
Instead of making and storing all sizes of capacitors, we can make and store just certain values of capacitors. When we need a non-standard size capacitor, we can make it by hooking two or more standard size capacitors together to make an effective capacitor of the value we need.
Two basic waysThere are two basic ways of connecting two capacitors:
series and parallel.
In series, we connect capacitors together like railroad cars; using parallel plate capacitors it would look like this:
+ - + -
high V low V
C1 C2
Series
If we include a battery as the voltage source, the series circuit would look like this:
C1
+
Vbat
C2
Note that there is only one way around the circuit, and you have to jump BOTH capacitors in making the circuit - no choice!
ParallelIn a parallel hook-up, there is a branch point that
allows you to complete the circuit by jumping over either one capacitor or the other: you have a choice!
High V C1 Low V
C2
Parallel Circuit
If we include a battery, the parallel circuit would look like this:
+ + +
Vbat C1 C2
Formula for Series:
To see how capacitors combine to give an effective capacitance when in series, we can look either at C = Q/V, or at
C plate = A /d
Formula for SeriesUsing C = Q/V, we see that in series the charge moved
from capacitor 2’s negative plate must be moved through the battery to capacitor 1’s positive plate.
C1
+ +Q
Vbat C2
- -Q ( +Qtotal)
Formula for SeriesBut the positive charge on the left plate of C1 will attract a negative charge
on the right plate, and the negative charge on the bottom plate of C2 will attract a positive charge on the top plate - just what is needed to give the negative charge on the right plate of C1. Thus Qtotal = Q1 = Q2 .
C1 (+Q1 )
+ +Q1 -Q1 +Q2
Vbat C2
- -Q2
( +Qtotal)
Formula for Series
Also, the voltage drop across the two capacitors add to give the total voltage drop:
Vtotal = (V1 + V2).
Thus, Ceff = Qtotal / Vtotal = Qtotal / (V1 + V2), or (with Qtotal = Q1 = Q2)
[1/Ceff] = (V1 + V2) / Qtotal = V1/Q1 + V2/Q2 =
1/C1 + 1/C2 = 1/Ceffective
Parallel CircuitFor parallel, both plates are across the same voltage, so Vtotal =
V1 = V2 . The charge can accumulate on either plate, so: Qtotal = (Q1 + Q2).
Since the Q’s are in the numerator, we have:
Ceff = C1 + C2.
+ +Q1 +Q2
Vbat C1 -Q1 C2 -Q2
+Q1
+Qtotal = (Q1+Q2) +Q2
Review of FormulasElectric Current I= ΔQ/Δt
Resistor Voltage Drop V = IR
Resistivity R =/A
Electric Power P = IV
Resistance Power P = I2R = V2/R
Junction Law I = I in out
Loop Law ΔV = loop
Series Resistors Rs = R1 + R2 +…
Parallel Resistors 1/RP = 1/R1 + 1/R2 +…
Terminal Voltage VT = VB ± IR
Capacitance C = Q/V
Parallel Plate Capacitor C plate A / d∝
Capacitors in Series 1/Cs = 1/C1 + 1/C2 +…
Capacitors in Parallel CP = C1 + C2 +…
Energy in Capacitor U = ½ Q2 /C = ½ CV2 = ½ QV
1/Ceff = 1/C1 + 1/C2 .
For capacitors in PARALLEL we have:
Ceff = C1 + C2 .
Note that adding in series gives Ceff being smaller than the smallest, while adding in parallel gives Ceff being larger than the largest!