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Norton's Theorem Norton's theorem for electrical networks states that any collection of voltage sources and resistors with two terminals is electrically equivalent to an ideal current source I in parallel with a single resistor R. The theorem can also be applied to general impedances, not just resistors. The theorem was published in 1926 by Bell Labs engineer Edward Lawry Norton (1898-1983). To calculate the equivalent circuit: - Replace the load circuit with a short.
- Calculate the current through that short, I, from the original sources.
- Now replace voltage sources with shorts and current sources with open circuits.
- Replace the load circuit with an imaginary ohm meter and measure the total resistance, R, with the sources removed.
- The equivalent circuit is a current source with current I in parallel with a resistance R in parallel with the load.
In the example, the total current Itotal is given by: -
I_\mathrm{total} = {15 \mathrm{V} \over 2\,\mathrm{k}\Omega + 1\,\mathrm{k}\Omega \| (1\,\mathrm{k}\Omega + 1\,\mathrm{k}\Omega)} = 5.625 \mathrm{mA} The current through the load is then: -
I = {1\,\mathrm{k}\Omega + 1\,\mathrm{k}\Omega \over (1\,\mathrm{k}\Omega + 1\,\mathrm{k}\Omega + 1\,\mathrm{k}\Omega)} \cdot I_\mathrm{total} -
= 2/3 \cdot 5.625 \mathrm{mA} = 3.75 \mathrm{mA} And the equivalent resistance looking back into the circuit is: -
R = 1\,\mathrm{k}\Omega + 2\,\mathrm{k}\Omega \| (1\,\mathrm{k}\Omega + 1\,\mathrm{k}\Omega) = 2\,\mathrm{k}\Omega So the equivalent circuit is a 3.75 mA current source in parallel with a 2 kΩ resistor. See also External links
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