An ideal 9V voltage source is connected to three different resistive loads: 10Ω, 100Ω, and 1kΩ. What remains constant across all three connections?
AThe current supplied to each load (all three draw the same current)
BThe power delivered to each load (all three consume the same power)
CThe terminal voltage of the source (it stays at 9V regardless of load)
DThe internal resistance of the source, which adjusts to stabilize the output
By definition, an ideal voltage source maintains a fixed potential difference across its terminals regardless of what current the load demands. With 10Ω it supplies 0.9A (9W), with 100Ω it supplies 90mA (810mW), with 1kΩ it supplies 9mA (81mW). The current and power all differ; only the 9V terminal voltage stays constant. This is the defining property of an ideal voltage source: zero internal resistance means no voltage drop inside the source, so all of the source voltage appears at the terminals.
Question 2 Multiple Choice
A 10 mA ideal current source is connected first to a 100Ω load, then to a 10kΩ load. What changes between the two configurations?
AThe current through the load (it adjusts downward to stay within the source's rating)
BThe voltage across the source terminals (it rises from 1V to 100V to maintain 10mA)
CThe internal resistance of the current source (it adjusts to deliver constant current)
DNothing changes — an ideal current source behaves identically regardless of load
An ideal current source enforces constant current regardless of terminal voltage. With a 100Ω load, V = IR = (10mA)(100Ω) = 1V. With a 10kΩ load, V = (10mA)(10kΩ) = 100V. The current stays at 10mA; the voltage adjusts automatically. This is the dual of a voltage source: where a voltage source holds V constant and lets I vary, a current source holds I constant and lets V vary. The current source's infinite internal resistance is what allows it to present whatever voltage the circuit requires.
Question 3 True / False
An ideal current source, like an ideal voltage source, has zero internal resistance.
TTrue
FFalse
Answer: False
This reverses the duality. An ideal voltage source has zero internal resistance so that no voltage drops across its internal path — all voltage appears at the terminals regardless of current. An ideal current source has infinite internal resistance so that all current is forced through the external load — none is diverted through the internal path. Infinite internal resistance means the source resists any deviation from its specified current by presenting an arbitrarily high impedance. The two are exact duals: zero vs. infinite internal resistance, fixed voltage vs. fixed current.
Question 4 True / False
A real battery's terminal voltage drops as more current is drawn from it, which is why the ideal voltage source model is most accurate when the load resistance is much larger than the battery's internal resistance.
TTrue
FFalse
Answer: True
A real battery is modeled as an ideal voltage source in series with a small internal resistance r. The terminal voltage is V_terminal = V_source − I × r. When load resistance R_load >> r, the current I = V_source / (R_load + r) ≈ V_source / R_load is small, and the drop I × r is negligible. The terminal voltage ≈ V_source, and the ideal model is accurate. When a large current is drawn (small load resistance), I × r becomes significant, terminal voltage sags, and the ideal model breaks down. This is why batteries feel 'weak' under heavy load.
Question 5 Short Answer
What is a dependent source, and why must circuit analysis methods account for dependent sources when modeling transistors and operational amplifiers?
Think about your answer, then reveal below.
Model answer: A dependent (controlled) source has its output — voltage or current — set by another voltage or current elsewhere in the circuit, rather than being a fixed value. There are four types: voltage-controlled voltage source (VCVS), current-controlled voltage source (CCVS), voltage-controlled current source (VCCS), and current-controlled current source (CCCS). Transistors and op-amps are modeled using dependent sources because their behavior is inherently relational: a BJT's collector current is proportional to its base-emitter voltage (a VCCS with transconductance g_m), and an op-amp's output voltage is proportional to its differential input voltage (a VCVS with high gain). Without dependent sources, there is no way to represent amplification — the defining property of active devices.
This is why dependent sources are not a theoretical curiosity but the bridge between passive circuit analysis and electronics. Nodal and mesh analysis methods apply unchanged with dependent sources, but the dependent source's controlling quantity must be expressed in terms of node voltages or mesh currents — adding an algebraic constraint that ties parts of the circuit together. Mastering this is the prerequisite for analyzing any amplifier circuit.