FAQ
TL;DR: For this CCVS exam circuit, the max-power condition evaluates to R = 1 Ω; “io=-0.5A and R=1ohm.” [Elektroda, Anonymous, post #21681205]
Why it matters: If you’re revising how to pick R for maximum power with dependent sources, this FAQ shows the steps and pitfalls clearly—ideal for students and self-learners.
Quick Facts
- Final thread result: R = 1 Ω and io = −0.5 A at the operating point. [Elektroda, Anonymous, post #21681205]
- Diamond symbol denotes a dependent source; here it’s a current-controlled voltage source (CCVS). [Elektroda, Anonymous, post #21681199]
- The 1 Ω in series with a 1 A current source doesn’t affect DC; it’s distraction. [Elektroda, Anonymous, post #21681200]
- Dependent source makes the circuit nonlinear, complicating Thevenin use. [Elektroda, Anonymous, post #21681201]
- Edge case: if the center node drops below −1 V, the right current source sinks power. [Elektroda, Anonymous, post #21681198]
What exactly was the exam-style question here?
Determine R so the resistor receives maximum power, then compute that maximum power. The circuit mixes a current-controlled voltage source on the left and a 1 A source on the right, which makes analysis nontrivial. [Elektroda, Anonymous, post #21681193]
How do I pick R for maximum power in this circuit?
Use nodal or mesh analysis to express power in R as a function of R, then differentiate and set dP/dR=0. A participant concluded R = 1 Ω with io = −0.5 A after solving. “Way harder than it first appears,” but tractable. [Elektroda, Anonymous, post #21681205]
Can I just use the Thevenin maximum-power rule R = RTh?
Yes in principle, but extracting RTh with a CCVS is awkward. One poster instead wrote node equations, found P(R), and optimized directly. That avoided building a Thevenin model around a nonlinear dependent source. [Elektroda, Anonymous, post #21681200]
What final values did the solvers in the thread agree on?
They reconciled to io = −0.5 A and R = 1 Ω. This aligns with the computed operating point once sign conventions were corrected. [Elektroda, Anonymous, post #21681205]
Is the loop stable for positive R?
A later correction notes the loop gain is negative for all positive R, so the circuit is stable in that region. That addresses earlier concerns about instability claims. [Elektroda, Anonymous, post #21681209]
Is the left diamond source a voltage or current source?
It is a current-controlled voltage source (CCVS). The diamond marks dependency; the source’s voltage is proportional to a measured current, matching small-signal transistor modeling practice. [Elektroda, Anonymous, post #21681199]
Does the 1 Ω series resistor with the 1 A source matter?
No for DC analysis here. A 1 Ω in series with an ideal current source does not change the enforced 1 A; it’s present to distract. [Elektroda, Anonymous, post #21681200]
Why do folks say this question is difficult?
You must mix nodal/mesh methods and handle a dependent source. As one expert put it, it’s “way harder than it first appears,” especially under exam timing. [Elektroda, Anonymous, post #21681193]
How should I solve it step by step without Thevenin?
- Choose the bottom node as reference and write node voltages in terms of io and R.
- Write KCL at the center node; express all currents via node voltages.
- Substitute into P=V^2/R or I^2R for the load, differentiate P(R), set derivative to zero. [Elektroda, Anonymous, post #21681200]
What happens if the center node voltage drops below −1 V?
The right-hand 1 A source would absorb power instead of supplying it. That sign flip is an important edge case when checking power directions. [Elektroda, Anonymous, post #21681198]
Do current direction arrows define actual current direction?
They define reference direction. If your solved current is negative, actual current flows opposite the arrow. One solver found io negative, consistent with the diagram. [Elektroda, Anonymous, post #21681204]
Is there a quick heuristic for max power if I did have a Thevenin model?
Yes. For a linear Thevenin source, max power in the load occurs when Rload equals RTh. This rule of thumb guided one poster’s thinking before full analysis. [Elektroda, Anonymous, post #21681195]
Where can I review nodal and mesh methods fast?
See the referenced MIT OCW notes covering nodal and mesh analysis with worked steps. They’re concise and ideal for exam prep. “Nodal and Mesh Methods (MIT OCW)”
Where can I read a refresher on dependent sources?
The linked tutorial explains dependent voltage and current sources and their symbols, with CCVS examples you can mirror in hand analysis. [Electronics-Tutorials.ws]
What was the consensus about using simulators on this circuit?
Participants emphasized understanding first. After reconciling signs, the hand solution was consistent, and no special simulator tricks were required. [Elektroda, Anonymous, post #21681209]
