Questions: Voltage and Current Source Characteristics

Question 1

A real battery has an open-circuit voltage of 9 V and an internal resistance of 1 Ω. It is connected to a 2 Ω external load. What is the terminal voltage under load?

• A. 9 V — the battery maintains its rated voltage regardless of load
• B. 6 V — the internal resistance drops 3 V at 3 A of current
• C. 3 V — the voltage splits equally between internal and external resistance
• D. 4.5 V — the terminal voltage is always half the open-circuit voltage under load

Answer: (B)

Current flows: I = 9 V / (1 Ω + 2 Ω) = 3 A. The internal resistance drops I × r_s = 3 × 1 = 3 V. Terminal voltage = V_s − I·r_s = 9 − 3 = 6 V. Option A is the ideal voltage source behavior — a real source 'sags' under load because current through the internal resistance creates an internal voltage drop. This is why a weak battery may still read 9 V with no load but deliver less under load.

Question 2

An ideal current source is connected to a circuit. As the external load resistance increases from 10 Ω to 10 kΩ, what happens to the current delivered by the source?

• A. The current decreases proportionally as resistance increases (Ohm's law)
• B. The current remains constant at I_s; only the terminal voltage changes
• C. The current increases to compensate for the higher resistance
• D. The current drops to zero because the high resistance blocks current flow

Answer: (B)

An ideal current source maintains constant current I_s regardless of the terminal voltage or external resistance — this is its defining characteristic. The terminal voltage adjusts to whatever value is needed: V = I_s × R_load. This is the dual of an ideal voltage source (which maintains constant voltage regardless of current). Option A reflects Ohm's law thinking, which applies to resistors, not to current sources whose whole purpose is to fix the current.

Question 3

An ideal voltage source has zero internal resistance, meaning it can supply unlimited current at its rated voltage without any voltage drop.

• T. True
• F. False

Answer: True

By definition, an ideal voltage source maintains V_s at its terminals for any current, from zero to infinity. Zero internal resistance means no I·r_s drop. Of course, no real physical source achieves this — real sources have finite internal resistance that causes terminal voltage to sag under heavy current draw. The ideal model is an abstraction useful for circuit analysis when the internal resistance is negligible compared to the load.

Question 4

A real battery with significant internal resistance will deliver higher terminal voltage when supplying heavy current than when supplying light current.

• T. True
• F. False

Answer: False

The opposite is true. Terminal voltage = V_s − I·r_s. As current I increases, the drop I·r_s increases, so terminal voltage decreases. A heavily loaded battery delivers less voltage than the same battery under light load. This is why car headlights dim briefly when you start the engine (starter motor draws huge current), and why a weak battery's terminal voltage 'collapses' under load even if it reads near full voltage when idle.

Question 5

What is internal resistance in a real battery, and why does it cause the terminal voltage to be lower than the open-circuit (rated) voltage when current is flowing?

Model answer: Internal resistance r_s represents the resistance within the battery itself — arising from electrode chemistry, electrolyte conductivity, and contact resistance. When current I flows, Ohm's law requires a voltage drop I·r_s across this internal resistance. The terminal voltage (available to the external circuit) is V_terminal = V_s − I·r_s, which is less than the ideal open-circuit voltage V_s. A larger current draw causes a larger internal drop and a lower terminal voltage.

The model 'ideal voltage source + series internal resistance' is also the basis for Thévenin equivalent circuits: any two-terminal network with sources and resistors can be reduced to exactly this form. Understanding that real sources sag under load is essential for battery selection, motor drive circuits, and any application where significant current will be drawn.