Norton's Theorem - Example of A Norton Equivalent Circuit

Example of A Norton Equivalent Circuit

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, using the current divider rule:

I = {1\,\mathrm{k}\Omega + 1\,\mathrm{k}\Omega \over (2\,\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_\mathrm{eq} = 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.

Read more about this topic:  Norton's Theorem

Famous quotes containing the words norton, equivalent and/or circuit:

    “Every cloud must have a silver lining.”
    —George A. Norton (1880–1923)

    “Perhaps basketball and poetry have just a few things in common, but the most important is the possibility of transcendence. The opposite is labor. In writing, every writer knows when he or she is laboring to achieve an effect. You want to get from here to there, but find yourself willing it, forcing it. The equivalent in basketball is aiming your shot, a kind of strained and usually ineffective purposefulness. What you want is to be in some kind of flow, each next moment a discovery.”
    —Stephen Dunn (b. 1939)

    “Within the circuit of this plodding life
    There enter moments of an azure hue,
    Untarnished fair as is the violet
    Or anemone, when the spring strews them
    By some meandering rivulet, which make
    The best philosophy untrue that aims
    But to console man for his grievances.
    I have remembered when the winter came,”
    —Henry David Thoreau (1817–1862)