Lecture 22
March 2, 2016
Electrical Circuits
Series or parallel that’s the question.
Current, Power and Energy
Why does my laptop battery die?
Transmission of power to your home
Why do we have big transmission towers?
Household Appliances
Why do fuses blow?
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Physics 214 Spring 2016
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Electrical power and energy
In order to separate charges we have to do work
𝑾 = 𝑭. 𝒅 and energy is stored as potential energy
increase ΔV. The simplest example is a battery.
The quantity we call voltage is related to the
energy stored
ΔV = ΔPotential Energy/q (joules/coulomb = volt)
When positive charge moves to the negatively
charged plate or vice versa then the stored
energy is released. In order for this to happen the
two sides of the battery must be joined by a
conductor so that the charge can move easily.
This is a simple electric circuit.
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Electrical circuits
All circuits have an external source
of energy which provides a voltage.
In our case, it is a battery.
In a charged battery there is
separation of charge. When the
circuit is made, positive charge flows
from high to low voltage or negative
charge flows from low to high
voltage, releasing the stored energy.
Normally it is electrons which flow.
As they move they “collide” with the
atoms of the wire and lose some of
their energy in the form of heat.
There is resistance to the flow.
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Current and resistance
The rate of flow of charge is called current and it
is denoted by I
I = q/t amperes (coulombs/sec)
The direction of I is the flow of positive charge or
opposite to the flow of negative charge.
OHM’s Law
or equivalently
R = ΔV/I
ΔV= I R
ohms
The potential drop ΔV over a resistance R is the
current times the resistance.
Every part of a circuit has resistance including an
internal resistance in the battery. The higher the
resistance the lower is the current for a given
voltage difference
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Electromotive force
The electromotive force of a battery , ε ,
is the voltage difference between the two
terminals when no current is flowing.
When the battery is connected to a
simple circuit, as in the figure on the right
I = ε/(Rcircuit + Rbattery)
where Rbattery is the internal resistance of
the battery.
A voltage difference is the energy stored
or the energy released per unit charge.
So if charge +q goes from high to low
voltage then the energy released by the
battery is qε or qΔV
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Series circuit
If we add more light bulbs in the circuit in series the total resistance
increases and the current will be reduced. The current is the same in
all parts of the circuit and the voltage difference across each identical
light bulbs is the same
ε = I(Rbattery + R + R + R)
The voltage difference across any light = IR
The total resistance of the circuit is the sum of all
resistances. If one bulb is broken, the current stops
flowing. These are the general characteristics of all series
circuits.
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Parallel circuit
The current q at A
divides into three and
then recombines at B
In the circuit shown the voltage difference across each light is the same
and the total current is the sum of the three currents
I = I1 + I2 + I3 and since a current = ΔV /R
ΔVAB /Rcircuit = ΔVAB /R1 + ΔVAB /R2 + ΔVAB /R3
and
1/Rcircuit = 1/R1 + 1/R2 + 1/R3
That is the total resistance of the circuit is smaller than any of the single
resistances. It is also true that if one bulb fails the other two will stay lit
at the same brightness.
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What is voltage?
We have seen that the definition of voltage is
ΔV = Δpotential energy/q when a charge q is moved in an
electrical force field. So energy is stored as potential energy as a
positive charge is moved in the opposite direction to E or a
negative charge is moved in the same direction as E.
If we move a positive charge toward a positive charge potential
energy and ΔV increase or if we move a negative charge away
from a positive charge.
Just as in the gravitational field there are only differences in PE.
So normally we use the term ΔV. But very often for circuits we
choose one point, usually the negative terminal, to be zero and
then instead of ΔV we just use V.
When charge is free to move, that is positive charge moving to a
lower voltage or negative charge moving to a higher voltage the
PE will transform into KE just like dropping something. In a simple
circuit with resistance this KE is turned into heat and light so
there is a voltage drop across every element in the circuit.
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Voltage drop
If we have a circuit with many different
resistors then there is a voltage drop
across each resistor and there is also a
voltage drop for the whole circuit.
Current only flows if there is a voltage
difference and in a time t charge q
passes through the resistor.
I = q/t and ΔV = IR
Case1
6V
1 V
I
60 

10 
 0.1A
V15  15   0.1A, V20  20   0.1A, V25  25   0.1A
Case 2
I 24 
12 V
, I total  3I 24  3  0.5A  1.5A
24 
Case 3 Rtotal  R23  R13  R33
1
1
1
2



,
R23 3  3  3 
Rtotal
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1
1
1
1
3




R33 3  3  3  3 
V
 1.5   3   1   5.5 , I  AB
5.5 
V23  IR23 
VAB 3
3V
  AB
5.5  2
11
V33  IR33 
VAB 3
V
  AB
5.5  3
5.5
VAB
3VAB
V

IR

3


31
31
Physics 214 Spring 2016
5.5 
5.5
9
Series plus parallel
A
I
V
I1
R1
R2
I2
I3
A
B
R3
I
I
I
Rparallel
R4
R4
B
VAB = I1R1
VAB = I2R2
VAB = I3R3
I = I1 + I2 + I3
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V
B
Physics 214 Spring 2016
V4 = IR4
V = VAB + V4
V = I(R4 + Rparallel)
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