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Internal Resistance of a Source Definition: The resistance within a battery, or other voltage...

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Internal Resistance of a Source Definition: The resistance within a battery, or other voltage source, that causes a drop in the source voltage when there is a current . Lecture 3
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Page 1: Internal Resistance of a Source Definition: The resistance within a battery, or other voltage source, that causes a drop in the source voltage when there.

Internal Resistance of a Source

Definition:

The resistance within a battery, or other voltage source, that causes a drop in the source voltage

when there is a current .

Lecture 3

Page 2: Internal Resistance of a Source Definition: The resistance within a battery, or other voltage source, that causes a drop in the source voltage when there.
Page 3: Internal Resistance of a Source Definition: The resistance within a battery, or other voltage source, that causes a drop in the source voltage when there.
Page 4: Internal Resistance of a Source Definition: The resistance within a battery, or other voltage source, that causes a drop in the source voltage when there.

The battery internal resistance

=

๐‘‰ ๐ฟ=๐‘‰ ๐‘ก=๐‘‰ ๐‘›๐‘™โˆ’ ( ๐ผ๐ฟร—๐‘Ÿ )= ๐ผ๐ฟร—๐‘…๐ฟ

Page 5: Internal Resistance of a Source Definition: The resistance within a battery, or other voltage source, that causes a drop in the source voltage when there.

Maximum Power Transfer Theorem

๐œ€=๐‘‰ ๐‘›๐‘™

๐‘…๐‘–๐‘›๐‘ก

๐‘ป๐’‰๐’†๐’Ž๐’‚๐’™๐’Š๐’Ž๐’–๐’Ž๐’‘๐’๐’˜๐’†๐’“ ๐’•๐’“๐’‚๐’๐’”๐’‡๐’†๐’“ ๐’•๐’‰๐’†๐’๐’“๐’†๐’Ž ๐’”๐’•๐’‚๐’•๐’†๐’”๐’•๐’‰๐’‚๐’• :

Page 6: Internal Resistance of a Source Definition: The resistance within a battery, or other voltage source, that causes a drop in the source voltage when there.

๐œ€=๐‘‰ ๐‘›๐‘™

๐‘…๐‘–๐‘›๐‘ก

Page 7: Internal Resistance of a Source Definition: The resistance within a battery, or other voltage source, that causes a drop in the source voltage when there.

๐œ€=๐‘‰ ๐‘›๐‘™

๐‘…๐‘–๐‘›๐‘ก

It is clear that . If the load power calculated for a range of variation of load resistance from 0.1 ฮฉ to 30 ฮฉ, and plotted as shown in the figure , then this will lead to a certain conclusion.

Page 8: Internal Resistance of a Source Definition: The resistance within a battery, or other voltage source, that causes a drop in the source voltage when there.

This table represents the values of the output power, the load current and load voltage

Page 9: Internal Resistance of a Source Definition: The resistance within a battery, or other voltage source, that causes a drop in the source voltage when there.

This plot shows the load power as a function of load resistance

Page 10: Internal Resistance of a Source Definition: The resistance within a battery, or other voltage source, that causes a drop in the source voltage when there.

This plot shows the variation of load voltage and current with load resistance

Page 11: Internal Resistance of a Source Definition: The resistance within a battery, or other voltage source, that causes a drop in the source voltage when there.

The plotted results shows that the maximum load power occurs when the load resistance equal to the internal resistance. Also, it shows that the variation in power is very steep when . This can be verified due to the steep change in load voltage and load current in the same region. Since:

=Where is the power dissipated inside the source due to its internal resistance, then:

This equation means when , tends to . But in this case the power in the circuit will be very small, as shown in the proceeding slide.

Page 12: Internal Resistance of a Source Definition: The resistance within a battery, or other voltage source, that causes a drop in the source voltage when there.

This plot shows the truth that when , tends to , While the following relation show the reduction in output power at this case.

Page 13: Internal Resistance of a Source Definition: The resistance within a battery, or other voltage source, that causes a drop in the source voltage when there.

๐‘ƒ๐‘ =๐‘‰ ๐‘›๐‘™ร— ๐ผ ๐ฟ

๐‘ƒ (W )

๐‘…๐ฟ=๐‘… ๐‘–๐‘›๐‘ก=9ฮฉ

๐‘ƒ ๐ฟ๐‘š๐‘Ž๐‘ฅ

๐‘ƒ ๐ฟ

๐‘…๐ฟ (ฮฉ )๐‘…๐ฟ=๐‘… ๐‘–๐‘›๐‘ก=9ฮฉ

This leads to the fact that the best operating condition is that, when the load resistance equal to the internal resistance of the source, form the view point of maximum power transfer from source to load.

Page 14: Internal Resistance of a Source Definition: The resistance within a battery, or other voltage source, that causes a drop in the source voltage when there.

New and Renewable Energy Sources

Photovoltaic Panel(PV) Panel

And Wind Energy

Page 15: Internal Resistance of a Source Definition: The resistance within a battery, or other voltage source, that causes a drop in the source voltage when there.

The Solar Energyโ€ข The Photovoltaic Panel is no more than an energy transducer. It has an ability

to generate electric energy from solar energy. It is one of the renewable energy sources. It is cheap, clean and available.

โ€ข The most important property to be considered, is that โ€œit has a non-linear internal resistanceโ€. This property is shown in the figures below:

Page 16: Internal Resistance of a Source Definition: The resistance within a battery, or other voltage source, that causes a drop in the source voltage when there.

โ€ข The V/I characteristics shows that this source has a nonlinear internal resistance as compared with that of the battery. Then its output power has a maximum value at one point only as shown in the P/V characteristics shown above.

Page 17: Internal Resistance of a Source Definition: The resistance within a battery, or other voltage source, that causes a drop in the source voltage when there.

PV Array characteristics at different irradiation levels

Note: Such a source needs special arrangements in order to achieve the maximum power point. This is done by changing the value of the input load resistance continuously in order to follow the source internal resistance.


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