Concept explainers
(a) Obtain a value for the Thévenin equivalent resistance seen looking into the open terminals of the circuit in Fig. 5.76 by first finding Voc and Isc. (b) Connect a 1 A test source to the open terminals of the original circuit after shorting the voltage source, and use this to obtain RTH. (c) Connect a 1 V test source to the open terminals of the original circuit after again zeroing the 2 V source, and use this now to obtain RTH.
FIGURE 5.76
(a)
Find the value for the Thevenin’s equivalent resistance seen looking into the open terminals of the circuit by first finding
Answer to Problem 35E
The Thevenin’s equivalent resistance is
Explanation of Solution
Calculation:
The redrawn circuit diagram is given in Figure 1.
Apply KCL ay node 1,
Here,
Substitute
Rearrange for
Apply KCL at node 2,
Here,
Substitute
Rearrange for
Substitute
Rearrange for
Substitute
So, the voltage
The redrawn circuit diagram is given in Figure 2,
Refer to the redrawn Figure 2,
Apply KCL at node 1,
Substitute
Rearrange for
Apply KCL at node 2,
Here,
Substitute
Rearrange for
Substitute
The expression for the current flowing through
Here,
Substitute
So, the current
The expression for the Thevenin’s equivalent resistance is as follows,
Here,
Substitute
Conclusion:
Thus, the Thevenin’s equivalent resistance is
(b)
Connect a
Answer to Problem 35E
The Thevenin’s equivalent resistance is
Explanation of Solution
Calculation:
The redrawn circuit diagram is given in Figure 3,
Refer to the redrawn Figure 3,
Apply KCL ay node 1,
Here,
Substitute
Rearrange for
Apply KCL at node 2,
Here,
Substitute
Rearrange for
The expression for the current flowing through
Here,
Substitute 1 A for
Rearrange for
Substitute
Substitute
Rearrange for
Substitute
The expression for the Thevenin’s equivalent resistance is as follows,
Here,
Substitute 35.43 V for
Conclusion:
Thus, the Thevenin’s equivalent resistance is
(c)
Connect a 1 V test source to the open terminals of the original circuit after again
zeroing the 2 V source, and use this now to obtain
Answer to Problem 35E
The Thevenin’s equivalent resistance is
Explanation of Solution
Calculation:
The redrawn circuit diagram is given in Figure 4,
Refer to the redrawn Figure 4,
Apply KCL ay node 1,
Here,
Substitute
Rearrange for
Apply KCL at node 2,
Here,
Substitute
Rearrange for
Substitute
The expression for the Thevenin’s equivalent resistance is as follows,
Here,
Substitute 0.1532 V for
Conclusion:
Thus, the Thevenin’s equivalent resistance is
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Chapter 5 Solutions
Loose Leaf for Engineering Circuit Analysis Format: Loose-leaf
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