Concept explainers
For the circuit in Fig. 4.109, find the Thevenin equivalent between terminals a and b.
Figure 4.109
Find the Thevenin voltage and Thevenin resistance at terminals a-b of the circuit shown in Figure 4.109.
Answer to Problem 42P
The Thevenin voltage is
Explanation of Solution
Given data:
Refer to Figure 4.109 in the textbook.
The voltage source is
The current source is
Calculation:
In the given circuit, find the Thevenin resistance by turning off
The modified circuit is shown in Figure 1.
In Figure 1,
The modified circuit is shown in Figure 2.
In Figure 2, the three
For the delta connection in Figure 3, the value of the resistor
Similarly,
And,
The modified circuit is shown in Figure 4.
In Figure 4,
The modified circuit is shown in Figure 5.
In Figure 5, the Thevenin resistance is,
Refer to Figure 4.109 in the textbook.
The given circuit is modified as shown in Figure 6.
In Figure 6, the voltage source with series resistance is converted into current source with parallel resistance by source transformation method.
That is,
Similarly, the current source with parallel resistance is converted into voltage source with series resistance by source transformation method.
That is,
The source transformation is shown in Figure 7.
In Figure 7,
The modified circuit is shown in Figure 8.
In Figure 8, the current source with parallel resistance is converted into voltage source with series resistance by source transformation method.
That is,
The source transformation is shown in Figure 9.
In Figure 9, apply Kirchhoff’s voltage law to the loop
Rearrange the equation (1) as follows,
In Figure 9, apply Kirchhoff’s voltage law to the loop
Substitute
Substitute 0 for
In Figure 9, apply Kirchhoff’s voltage law to the outer loop as follows.
Substitute 0 for
Since, the voltage
The Thevenin equivalent is shown in Figure 10.
Conclusion:
Thus, the Thevenin voltage is
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