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CHAPTER 19

CURRENT, RESISTANCE AND

ELECTROMOTIVE FORCE

BASIC CONCEPTS

CURRENT and CURRENT DENSITY

RESISTANCE and RESISTIVITY

BATTERY INTERNAL RESISTANCE

ENERGY AND POWER IN CIRCUITS

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CURRENT IS THE MOVEMENT OF CHARGE

IN A MATERIAL

In some cases the objects that are moving

are positive.

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In other cases, for example in metals, the

objects are negative (electrons).

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Current is the time rate of passage of the

charge.

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RESISTIVITY

Resistivity, ρ, is a characteristic of a

material.

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RESISTIVITY

Resistivity, ρ, changes with temperature.

���� = ���1 + �� − ����

Where �� is the value at 200 C.

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For a metal:

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For Semiconductor:

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Some materials loose all resistivity –

Superconductors:

Discovered in 1911 by H. Kammerlingh

Onnes.

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RESISTANCE

Resistance is a characteristic of an object.

Resistance, R, is related to Resistivity, ρ, by

= ��

�

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The longer the object the higher the

resistance.

The larger the cross-section the smaller the

resistance.

If ρ is constant the total current through a

conductor is proportional to the voltage

across it.

� ∝ �

Or

� ∝ �

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The constant of proportionality is the

resistance, R.

� = �

Or

� = �

This is Ohm’s Law.

If a resistor obeys Ohm’s Law it is an Ohmic

resistor.

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Obeys Ohm’s Law:

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Semiconductors are not Ohmic:

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POWER DISIPATED WITH CURRENT FLOW.

Remember

q

V

Change in energy ∆�

∆� = ��

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� = �

Or � =�

�

� = ��

� = ��

� =��

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CALCULATE RESISTANCE

A copper rod with cross section A has a

length L what is its resistance? Work for

� = 3.14�10� !� and � = 10!.

From Table 25.1 � = 1.72�10�$Ω!

Therefore

= ��

�= �1.72�10�$Ω!�

10!

3.14�10� !�

= 5.48�10��Ω

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The figure is of a 12 V battery with no

current in the circuit.

The voltmeter will read 12 V.

But if there is current:

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The voltmeter will read less than 12 V.

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What is the current in the circuit?

� = �

� =�

=

12

4 + 2= 2�

What will the voltmeter read?

�()*+ = 12� − � ,-.)(-*/

�()*+ = 12� − �2���2Ω�

�()*+ = 12� − 4� = 8�

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DIRECT-CURRENT CIRCUITS

BASIC CONCEPTS

Resistors in circuits.

Kirchhoff’s Rules

Ammeters and Voltmeters

R-C Circuits

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In Chapter 24 we found equivalent

capacitance for combinations of capacitors.

1

0)1=

1

02+

1

0�456786987

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0)1 = 02 + 0�456:;6;<<8<

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For resistors we need similar equations.

The current I through each R is same.

The voltage �*= = �*> + �>? + �?=

And � = �

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Therefore

� 2 + � � + � @ = � )1A,B*/)-.

Can replace the three resistors with one

resistor with resistance )1A,B*/)-.

)1A,B*/)-. = 2 + � + @456786987

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The total current I is divided between

2, �, ;DE @

� = �2 + �� + �@

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And

� =�

Therefore

�

�FGHIJKLFMN=

�

�O+

�

�P+

�

�Q

Or

1

)1A,B*/)-.=

1

2+

1

�+

1

@

For Parallel.

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Consider the following circuit.

What is the current through the 6 Ω

resistor?

12V

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��R =��R

2Ω=12�

2Ω= 6�

Therefore there are 6A through the 1Ω

resistor.

�2T = �2R1Ω = 6�1Ω = 6�

The emf of the battery is

U = �2T + ��R = 6� + 12� = 18�

The current through the 6Ωresistor is

� R =U

6Ω=18�

6Ω= 3�

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Example:

1.25A

What does the voltmeter read?

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KIRCHHOFF’S RULES

Junction Rule

The sum of the currents into a junction is

zero.

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Loop Rule

The sum of the potential differences in a

loop is zero.

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Sign Convention

For resistors:

For batteries:

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Example:

Loop 1 (start at a)

−�� + U2 − �262 = 0

Loop 2 (start at c)

+U2 − �262 − ��6� − U� = 0

I1

I2

IR

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Loop 3 (start at a)

−�� + U� + ��6� = 0

Junction a

�2 = �� + ��

Junction b

�� + �� = �2