Math Problem Statement
Solution
To calculate the Thevenin resistance for the network given between points a and b, we'll follow these steps:
-
Turn off all independent sources:
- The 20V voltage source will be replaced by a short circuit.
- The 6A current source will be replaced by an open circuit.
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Simplify the resulting circuit: After deactivating the sources, the 5Ω and 20Ω resistors will remain, along with the 3Ω resistor between points a and b. We can now calculate the equivalent resistance seen between points a and b.
Step-by-step calculation:
- The 5Ω and 20Ω resistors are in parallel, so their equivalent resistance is:
- Now, this 4Ω equivalent resistance is in series with the 3Ω resistor between points a and b, giving the total Thevenin resistance :
Conclusion:
The Thevenin resistance between points a and b is .
Would you like more details or have any questions?
Here are some related questions:
- How would the calculation change if there were additional resistors between points a and b?
- What would happen if the current source were kept active while calculating ?
- How would you calculate the open-circuit voltage in this circuit?
- Can we apply the same method to a circuit with dependent sources? How?
- What happens if we swap the 20Ω resistor with an inductor? How does that affect the time-domain response?
Tip: When deactivating sources, always remember to short-circuit voltage sources and open-circuit current sources.
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Math Problem Analysis
Mathematical Concepts
Thevenin's Theorem
Resistors in Series and Parallel
Circuit Analysis
Formulas
Parallel Resistance: R_eq = (R1 * R2) / (R1 + R2)
Series Resistance: R_total = R1 + R2
Theorems
Thevenin's Theorem
Suitable Grade Level
Undergraduate Engineering or Advanced High School
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