Circuit Theory
NCEA AS2.6
Text Chapters:
Electric Current
A flow of electric charge is called an electric
current.
Current I is measured by the rate at which
electric charge flows
Current = charge/time
I = Q/t
Unit: Ampere (Amp) A
So 1A=1Cs-1
Current direction is defined as the direction of
positive charge flow.
Voltage
Current will only flow continuously if there
is a closed circuit.
To get the charges to flow, they need to
experience the force of an electric field.
To set up a field, we apply a voltage or
potential difference to the circuit.
Voltage
A voltage V is a measure of the difference
in potential energy of the charge between
two points in a circuit.
Voltage=Energy/Charge
V=E/Q
So 1V=1JC-1
A voltage can be positive or negative. ie
energy gain or energy loss.
Resistance
All materials have a certain amount of
electrical resistance R.
This inhibits the flow of charge and uses
up the charge’s energy.
A material with very high R is called an
insulator.
A material with very low R is called a
conductor.
Resistance is measured in Ohms W.
Resistance
Resistance is directly proportional to
Length. Longer = more resistance……
Resistance is inversely proportional to the
cross-sectional area. Thicker = less
resistance
Resistance is directly proportional to the
resistivity r of the material
In summary: R=Lr/A
Ohm’s Law
Current, voltage and resistance are linked
by Ohm’s Law: V=IR
This applies only to conductors that have
constant resistance.
Examples of non-Ohmic conductors
include diodes, lamps, thermistors and
LDRs.
Series and Parallel
If the components are linked one after the
other they are in series.
If they are linked alongside each other
they are in parallel
Series
Parallel
Meters
Ammeters measure current.
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Connected in series so that all the charge flows
through them
low R so that they do not use up the energy of the
charge.
BE CAREFUL – Ammeters are easy to damage.
Voltmeters measure voltage.
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Connected in parallel with the component they are
measuring the voltage drop/gain across.
High R so that they do not draw too much current
away from the circuit.
Combining Resistors
When connected in series, the total resistance
RT is the sum of the individual resistors:
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RT=R1+R2+R3….
This has the effect of increasing the resistance of the
circuit.
When connected in parallel, the total resistance
is found by adding reciprocals….
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1/RT= 1/R1+1/R2 +1/R3….
This has the effect of reducing the total resistance of
the circuit
Circuit Theory
Series Circuits:
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Current must be the same everywhere as
there is only one path for electrons to take.
Voltage must be shared by all resistors
4.5V
9.0V
4.5V
Circuit Theory
Parallel Circuits:
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Current can split to go down either pathway
Each resistor gets all the energy the charge is
carrying so voltage across each is the same
2A
4A
9V
9V
9V
2A
Parallel
Summary
Parallel
Series
Voltage
Same
Shared
Current
Shared
Same
Internal Resistance
Even components like batteries and
meters have resistance.
This means that even though a battery is
supposed to supply 9V for example, what
you get across it’s terminals may be less if
you try and draw a large current from it.
The battery’s resistance uses some of the
energy.
Potential Dividers
Used to control voltage of parts of a circuit
Works great as long as the load resistor is
large compared to divider resistors.
(Why??)
Vout= R2/(R1+R2)xVsource
R1
Vs
R2
Vout
Power
Power = Energy/time
However V=E/Q & I=Q/t so combining them:

P = VxI = E/QxQ/t = E/t
Power is measured in Watts W
By substituting Ohm’s Law into the power
equation, it can also be written as:

P=I2R or P=V2/R
This shows that the higher the current the more
power dissipated as heat.
Electrical safety
1mA is the maximum safe current the
human body can take.
100mA probably fatal
R(dry skin)=10kW
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If 10V applied, I=1mA (safe)
If 240V applied I=24mA (hmmm)
R (wet skin)=1.2kW
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If 240V applied I=200mA (R.I.P)