Electric Circuit Theory Concept

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Why do we take ideal voltage source to have 0 impedance and ideal current source to have infinite impedance.
Please explain mathematically also!
 
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An ideal voltage source is a voltage source that does not "sag," or decrease in voltage, no matter how much current we pull from it. An ideal 12V source will always produce 12V, even if you pull a hundred billion amperes of current from it.

A real voltage source, on the other hand, has some finite, non-zero resistance associated with it. A model of a "real" voltage source is an ideal voltage source with a resistor in series with it. As the resistor becomes larger, the voltage source becomes less and less ideal -- if you pull large currents, a large voltage drop appears across the resistor, and the output voltage of the source sags.

If you make the resistor very small, or drive it all the way to zero, the "real" voltage source becomes an ideal voltage source. Thus, an ideal voltage source has zero series resistance, or zero impedance.

The same argument applies to current sources having infinite impedance. Can you make those arguments yourself? Remember that the model of a "real" current source involves an ideal current source with a resistor in parallel.

- Warren