Resistance
Dr Miguel Cavero
August 1, 2014
Resistance
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Resistance
Resistance is the term used in referring to the opposition of current in
conductors.
(Charge carriers are losing energy in moving through a conductor.)
The current through a given is related to the voltage (potential
difference) applied across the ends of the material.
In some cases, the current and the voltage across a material are
directly proportional.
∆V ∝ I
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Resistance
When the current and the voltage across a material are directly
proportional:
∆V = IR
where R is the resistance of the material.
The SI unit of resistance is the ohm, Ω (1 Ω = 1 V A−1 ).
The resistance of a conductor is defined as the ratio of the voltage
across the conductor and the current it carries:
R=
Resistance
∆V
I
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Ohm’s Law
For many materials, over a wide range of potential differences, the
voltage and the current through the material is constant.
This is the statement of Ohm’s Law: the potential difference across a
material is directly proportional to the current through it.
∆V = IR
R is constant, and independent of ∆V and I.
Ohm’s law is an empirical relationship - it is valid only for certain
materials (and for a certain range of voltages). Not all materials obey
Ohm’s Law.
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Ohm’s Law
Most metals obey Ohm’s Law. Materials that follow this relationship
between voltage and current are known as ohmic materials (or
conductors).
Materials such as semiconductors are nonohmic - the relationship
between current and voltage is non-linear.
A diode is an example of a semiconductor, where its nonohmic nature
is manipulated in an electronic circuit. A diode provides very little
resistance for current moving in one direction, but provides a large
resistance for current moving in the opposite way.
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Resistor Combinations
A resistor is a conductor that provides a specified resistance in an
electrical circuit.
There are different combinations of resistors in a circuit. The two
considered here (like with capacitors) are series and parallel.
As before, an equivalent resistance can be found for either
combination type.
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Resistors In Series
Four resistors in series are shown below.
What is the equivalent resistance Req ?
What is the total potential difference ∆V across the combination, in
relation to the potential difference across the individual resistors?
∆V = ∆V1 + ∆V2 + ∆V3 + ∆V4
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Resistors In Series
From the definition of resistance:
∆V
= ∆V1 + ∆V2 + ∆V3 + ∆V4
= I1 R1 + I2 R2 + I3 R3 + I4 R4
= IReq
The current I is the same through every resistor (connected in series)
since the same charge must flow each of the resistors.
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Resistors In Series
∆V
= ∆V1 + ∆V2 + ∆V3 + ∆V4
IReq = IR1 + IR2 + IR3 + IR4
∴ Req = R1 + R2 + R3 + R4
The equivalent resistance for a combination of resistors in series is the
sum of the individual resistances.
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Resistors In Parallel
For resistors in parallel, the current through each branch is not the
same.
The current splits into each branch, so that the total going in is equal to
the total current going out.
I = I1 + I2 + I3
What is the voltage (potential difference) across each branch?
The potential difference has to be the same.
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Resistors In Parallel
For resistors in parallel:
I = I1 + I2 + I3
V
V
V
=
+
+
Req
R1 R2
1
1
1
=
+
+
Req
R1 R2
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Resistance
V
R3
1
R3
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