Concept explainers
Determine the Norton equivalent of the circuit depicted in Fig. 5.74 as seen looking into the two open terminals. (b) Compute power dissipated in a 5 Ω resistor connected in parallel with the existing 5 Ω resistor. (c) Compute the current flowing through a short circuit connecting the two terminals.
(a)
Find the Norton equivalent of the circuit as seen looking into the two open terminals.
Answer to Problem 33E
The Norton current is
Explanation of Solution
Formula used:
The expression for voltage is as follows.
Here,
The expression for series combination of resistance is as follows.
Here,
The expression for parallel combination of resistance is as follows.
Here,
Calculation:
The circuit diagram is redrawn as shown in Figure 1.
Refer to redrawn Figure 1,
The expression for KVL in super mesh
Here,
Substitute
The expression for KVL in mesh
Here,
Substitute
The expression for current
Here,
Substitute
Rearrange equations(5),(7) and (9).
The equations so formed can be written in matrix form as,
Therefore, by Cramer’s rule,
The determinant of coefficient matrix is as follows.
The 1st determinant is as follows.
The 2nd determinant is as follows,
The 3rd determinant is as follows.
Simplify for
Simplify for
Simplify for
Substitute
So, the Thevenin voltage is
The circuit diagram is redrawn as shown in Figure 2.
As
Rearrange for
The circuit diagram is redrawn as shown in Figure 3.
As
The circuit diagram is redrawn as shown in Figure 4.
Refer to redrawn Figure 4,
As
Rearrange for
So, the Thevenin equivalent resistance across the branch
Thevenin equivalent resistance is same as the Norton equivalent resistance,
Hence,
The circuit diagram is redrawn as shown in Figure 5,
Refer to redrawn Figure 5,
Norton current is the current in the load resistor when load resistance is replaced by a short circuit.
The expression for the Norton current flowing in the circuit is as follows,
Here,
Substitute
Conclusion:
Thus the Norton current is
(b)
Find the power dissipated in a
Answer to Problem 33E
The power dissipated in a
Explanation of Solution
Given Data:
The load resistance is
Formula used:
The expression for the power dissipated in a resistor is as follows,
Here,
Calculation:
The circuit is drawn as shown in Figure 6,
Refer to redrawn Figure 6,
The simplified Norton equivalent of the circuit is drawn as shown in Figure 7,
Refer to redrawn Figure 7,
The expression for the current flowing through the load is as follows,
Substitute
Substitute
Conclusion:
Thus, the power dissipated in a
(c)
Find the current flowing through a short circuit connecting the two terminals.
Answer to Problem 33E
The current flowing through a short circuit connecting the two terminals is
Explanation of Solution
Calculation:
The current flowing through a short circuit connecting the two terminals is Norton current which is
So, the current flowing through a short circuit connecting the two terminals is
Conclusion:
Thus, the current flowing through a short circuit connecting the two terminals is
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Chapter 5 Solutions
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