You need to find the voltage delivered to load resistors of 10Ω, 47Ω, and 100Ω connected to a complex circuit. What is the advantage of finding the Thévenin equivalent first?
AYou still solve the circuit three times, but each solution is simpler because the Thévenin model has fewer nodes
BYou reduce the source network once to V_th and R_th, then use a simple voltage divider formula for each load — no re-solving required
CYou find V_th once, and R_th equals the smallest resistor in the source network
DYou cannot use Thévenin's theorem unless all three loads are connected simultaneously
The payoff of Thévenin equivalents is decoupling the source from the load. You solve the source network once to find V_th (open-circuit voltage) and R_th (Thévenin resistance). Then for any load R_L, V_load = V_th × R_L / (R_th + R_L) — a simple voltage divider. Changing the load never requires re-solving the source network. This is why Thévenin analysis is so widely used: it converts a complex multi-component problem into a trivial two-resistor calculation for every subsequent load variation.
Question 2 Multiple Choice
To find R_th for a circuit containing only independent sources, you 'zero' the sources. What does zeroing a voltage source and zeroing a current source mean physically?
ABoth become open circuits, since a zero-value source contributes nothing to the circuit
BVoltage sources become open circuits; current sources become short circuits
CVoltage sources become short circuits (wires); current sources become open circuits (breaks)
DBoth sources are removed entirely and their terminals are left disconnected
Zeroing sets a source's value to zero. A voltage source with 0 V enforces zero potential difference across its terminals — exactly what a short circuit (wire) does. A current source with 0 A passes no current — exactly what an open circuit (break) does. Reversing these (option B) is a very common error that produces an incorrect R_th. The physical interpretation: a dead voltage source is a wire; a dead current source is a gap.
Question 3 True / False
Thévenin's theorem works because a linear circuit produces a straight-line V-I relationship at any two terminals, and a voltage source in series with a resistor is precisely the minimal circuit with that characteristic.
TTrue
FFalse
Answer: True
Linearity means the terminal voltage V is a linear function of the current I drawn: V = V_oc − I·R_th. This is a straight line in V-I space. The intercept at I = 0 is V_th (the open-circuit voltage), and the slope magnitude is R_th. A voltage source V_th in series with R_th produces exactly this same straight-line V-I characteristic. Thévenin's theorem is therefore a direct consequence of linearity: any circuit satisfying superposition has a Thévenin equivalent, because linearity guarantees the straight-line terminal behavior.
Question 4 True / False
For a circuit that contains dependent sources, R_th can be found by zeroing the dependent sources and computing the resistance at the terminals.
TTrue
FFalse
Answer: False
Dependent sources cannot be zeroed — they are controlled by circuit variables (other voltages or currents), and setting them to zero removes relationships that are essential to the circuit's behavior, producing an incorrect R_th. For circuits with dependent sources, the correct procedure is: (1) zero only the independent sources, (2) apply a test voltage V_test (or current I_test) at the terminals, and (3) compute R_th = V_test / I_test from the resulting current (or voltage). The test-source method correctly accounts for dependent source behavior.
Question 5 Short Answer
Explain why Thévenin's theorem holds — why can any linear two-terminal circuit always be replaced by a voltage source and a single resistor?
Think about your answer, then reveal below.
Model answer: Because linearity guarantees that the terminal voltage V is a linear function of the terminal current I: V = V_oc − I·R_th. Any straight-line V-I relationship can be reproduced by a voltage source V_th in series with a resistor R_th. No more complex internal structure is needed — from the terminals' perspective, only these two numbers (V_th and R_th) matter. V_th is the open-circuit voltage (I = 0), and R_th is the slope of the V-I line.
This is why Thévenin's theorem applies to any linear circuit regardless of how many resistors, capacitors, inductors, or sources it contains internally — the linearity property guarantees the terminal behavior collapses to a straight line. The theorem is essentially saying: all the internal complexity contributes only two numbers externally. This same reasoning underlies Norton's theorem (a current source in parallel with R_th), which represents the same straight line using the other intercept (at V = 0) and the same slope.