Concept explainers
The Norton and Thevenin equivalent networks from node
Answer to Problem 3.71HP
The Thevenin equivalent Network is shown in Figure 6 and the Norton equivalent network is shown in Figure 4
Explanation of Solution
Calculation:
The given diagram is shown in Figure 1
To determine the Norton equivalent, short circuit the output terminals, Mark the values, current direction, and redraw the circuit.
The required diagram is shown in Figure 2
Apply KVL to the first loop.
Apply KVL to the second loop.
The equation for the Norton current is given by,
Substitute
To obtain the Norton resistance of the circuit, short circuit the voltage source, open circuit the current source and redraw the circuit.
The required diagram is shown in Figure 3
Form the above circuit the Norton impedance of the circuit is calculated as,
Substitute
Mark the values and draw the Norton equivalent circuit.
The required diagram is shown in Figure 4
To calculate the Thevenin voltage, remove the load resistance and redraw the circuit.
The required diagram is shown in Figure 5
From the above circuit the value of the current
Substitute
The expression for the value of the current
Substitute
The expression for the voltage across the resistor
Substitute
The expression for the voltage across the resistor
Substitute
From Figure (5), the expression for the Thevenin voltage is given by,
Substitute
The Thevenin and the Norton resistance of the circuit are equal, thus the expression for the Thevenin resistance is given by,
Substitute
Mark the values and draw the Thevenin equivalent of the circuit.
The required diagram is shown in Figure 6
Conclusion:
Therefore, the Thevenin equivalent Network is shown in Figure 6 and the Norton equivalent network is shown in Figure 4
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Chapter 3 Solutions
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