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Bonus exercise at the end!
Thevenin's and Norton's theorem is intuitively a way to create the same circuit but much simpler.
Formally, Thevenin's and Norton's Theorem are stated as follows:
Thevenin's Theorem: states that any linear circuit, no matter how complex, can be simplified to an equivalent circuit consisting of a single voltage source with a series of resistance connected to a load The voltage source and resistance are called Thevenin voltage and Thevenin resistance, respectively.
Norton's Theorem: similar to Thevenin's Theorem, it states that any linear circuit, no matter how complex, can be simplified to an equivalent circuit consisting of a single current source connected with a parallel resistance and parallel to a load. The current source and resistance are called Norton current and Norton resistance, respectively.
Let's learn how to calculate the Thevenin voltage, Thevenin resistance, Norton current, and Norton resistance. Norton resistance and Thevenin resistance are the same and calculated similarly.
Thevenin Equivalent Circuit:
The first step is always to isolate the load resistance. Second, calculate the Thevenin voltage by calculating the voltage drop where the load resistance was located. When calculating the Thevenin resistance, we must transform any independent voltage source with a short circuit and an independent current source with an open circuit. Finally, create a circuit where we have the Thevenin voltage in series with the Thevenin resistance and in series with load. Done.
Norton Equivalent Circuit:
Since the Norton and Thevenin resistors are calculated similarly, we will discuss how to calculate the Norton current source. After calculating the Thevening voltage and Thevenin resistance, use Ohm's Law. Another way to sum it up is to short the circuit where the load was and calculate the current flow. Finally, create a circuit where the Norton current is the source parallel to the Norton resistance and connected parallel with the load.
Example:
Consider the first circuit above (first row, first column). The load resistance is colored in blue. Thevenin's equivalent circuit is the circuit located in the first row and second column. Norton's equivalent circuit is the circuit located in the first row and third column.
Calculations are displayed in the second row: the first one being the Thevenin voltage, the second one being the Thevenin resistance (equivalently Norton resistance), and the third one the Norton current.
However, the exact values are the following: Thevenin voltage = V_TH = 442.5V, Thevenin resistance = R_TH = 2kOhms, Norton current = I_N = 221.25mA, and Norton resistance = R_N = R_TH = 2kOhm For the load values, the voltage drop across the 4kOhm resistor is 295V, and the current at the load is 73.75mA.
Bonus:
Try to sketch the Thevenin and Norton's Equivalent circuit for the circuit at the third row. The load resistor y colored in green. Also, find the exact load voltage and load current.
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