Concept explainers
Find the maximum power transferred to resistor R in the circuit of Fig. 4.135.
Figure 4.135
Calculate the maximum power delivered to the resistor R of the circuit shown in Figure 4.135.
Answer to Problem 69P
The maximum power delivered to the variable resistor R is infinity.
Explanation of Solution
Given data:
Refer to Figure 4.135 in the textbook.
The voltage source is 100 V.
Formula used:
Write the expression to find the power delivered to the resistor.
Here,
Calculation:
The given circuit is modified as shown in Figure 1.
In Figure 1, the voltage source with series resistance is converted into current source with parallel resistance using source transformation. The current (I) is calculated by using Ohm’s law.
The source transformation is shown in Figure 2.
In Figure 2, apply Kirchhoff’s current law at node voltage
Simplify the equation as follows,
In Figure 2, apply Kirchhoff’s current law at node voltage
Substitute
Simplify the equation as follows,
Substitute
Since, the voltage at node
Refer to Figure 4.135 in the textbook.
In the given circuit, find the short circuit current by shorting the resistor R.
The modified circuit is shown in Figure 3.
To find the short circuit current
Substitute 0 for
In Figure 3, apply Kirchhoff’s current law at node voltage
Substitute 0 for
The Thevenin resistance is,
Substitute
The negative equivalent resistance indicates that an active device (dependent source) presents in the circuit, since the circuit cannot have a negative resistance in a purely passive circuit. The negative resistance for the equivalent circuit means that both the resistance and the source will effectively delivers the power to load.
Since the resistance cannot be the negative, the correct answer will be
Conclusion:
Thus, the maximum power delivered to the variable resistor R is infinity.
Want to see more full solutions like this?
Chapter 4 Solutions
Fundamentals of Electric Circuits