Concept explainers
(a) Using the superposition theorem, determine the current through the 12
b. Convert both voltage sources to current sources and recalculate the current to the 12
c. How do the results of parts (a) and (b) compare?
Fig. 9.125
(a)
The current through
Answer to Problem 1P
The current through
Explanation of Solution
Given:
The resistors values are
The voltage sources are
Concept Used:
Elements in the series have the same current.
Elements in the parallels have the same voltage.
Superposition theorem states that in any linear bilateral network having more than one source response in any one of the branches is equal to algebraic sum of the responses caused by individual source while rest of the sources are replaced by their internal impedances.
Short circuit the voltage source and open circuit the current source.
If the resistors are in series, then the value of the equivalent resistance for N series resistors is
If the resistors are in parallel, then the value of the equivalent resistance for N series resistors is
The special case for only two parallel resistors is
Current:
Current division is used to express the current across one of several parallel resistors in terms of current across the combination:
If there are two resistors in parallel then the current across second resistor is
Calculation:
Firstly, short circuit the voltage source
Conclusion:
Hence, the current through
(b)
The current through
Answer to Problem 1P
The current through
Explanation of Solution
Given:
The resistors values are
The voltage sources are
Concept Used:
Elements in the series have the same current.
Elements in the parallels have the same voltage.
Superposition theorem states that in any linear bilateral network having more than one source response in any one of the branches is equal to algebraic sum of the responses caused by individual source while rest of the sources are replaced by their internal impedances.
Short circuit the voltage source and open circuit the current source.
If the resistors are in series, then the value of the equivalent resistance for N series resistors is
If the resistors are in parallel, then the value of the equivalent resistance for N series resistors is
The special case for only two parallel resistors is
Current:
Current division is used to express the current across one of several parallel resistors in terms of current across the combination:
If there are two resistors in parallel then the current across second resistor is
Calculation:
Conclusion:
Hence, the current through
(c)
Compare the results of both the part (a) and (b).
Answer to Problem 1P
The results are similar in both the part (a) and (b).
Explanation of Solution
Given:
The resistors values are
The voltage sources are
Concept Used:
Elements in the series have the same current.
Elements in the parallels have the same voltage.
Superposition theorem states that in any linear bilateral network having more than one source response in any one of the branches is equal to algebraic sum of the responses caused by individual source while rest of the sources are replaced by their internal impedances.
Short circuit the voltage source and open circuit the current source.
Calculation:
The results are similar in both the part (a) and (b).
Conclusion:
Hence, the results are similar in both the part (a) and (b).
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