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Consider the 30-Ω resistor in Fig. 4.134. First compute the Thevenin equivalent circuit as seen by the 30-Ω resistor. Compute the value of R that results in Thevenin equivalent resistance equal to the 30-Ω resistance and then calculate power delivered to the 30-Ω resistor. Now let R = 0 Ω, 110 Ω, and ∞, calculate the power delivered to the 30-Ω resistor in each case. What can you say about the value of R that will result in the maximum power that can be delivered to the 30-Ω resistor?
Figure 4.134
Find the Thevenin equivalent seen by the
Calculate the power delivered to the
Answer to Problem 68P
The Thevenin voltage is
The power delivered to the
Explanation of Solution
Given data:
Refer to Figure 4.134 in the textbook.
The current source is
The voltage source is
The Thevenin resistance
Calculation:
In the given circuit, find the Thevenin voltage by removing the 30 ohms resistor and the modified circuit is shown in Figure 1.
The modified circuit is shown in Figure 1.
In Figure 1, the current source with parallel resistance is converted into voltage source with series resistance using source transformation. The voltage V is calculated by using ohms law as follows,
The source transformation is shown in Figure 2.
In Figure 2, the Thevenin voltage is,
Refer to Figure 4.134 in the textbook.
In the given circuit, find the Thevenin resistance by turning off the
The modified circuit is shown in Figure 3.
In Figure 3, the Thevenin resistance is,
Substitute
Substitute 50 for R in equation (1) to find the Thevenin voltage in volts.
Substitute 50 for R in equation (2) to find the Thevenin resistance in ohms.
The Thevenin equivalent connected to the 30 ohms resistor is shown in Figure 4.
The power delivered to the 30 ohms resistor is,
Substitute 60 for
Consider the resistance
When
Substitute 0 for R in equation (2) to find the Thevenin resistance in ohms.
When
Substitute 0 for R in equation (1) to find the Thevenin voltage in volts.
When
Substitute
Consider the resistance
When
Substitute 110 for R in equation (2) to find the Thevenin resistance in ohms.
When
Substitute 110 for R in equation (1) to find the Thevenin voltage in volts.
When
Substitute
Consider the resistance
When
Simplify equation (2) as follows,
Substitute
When
Simplify equation (1) as follows,
Substitute
When
Substitute
Thus, when
Conclusion:
Thus, the Thevenin voltage is
The power delivered to the
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Chapter 4 Solutions
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