How is the Norton current I_N determined when finding the Norton equivalent of a linear circuit at a pair of terminals?
ABy measuring the open-circuit voltage across the terminals with no load connected
BBy short-circuiting the terminals with a wire and measuring the current that flows through that short
CBy killing all independent sources and measuring the resistance seen from the terminals
DBy dividing the open-circuit voltage by the internal source resistance
The Norton current is defined as the short-circuit current — the current delivered into a zero-resistance (shorted) load. This is found by connecting a wire directly across the terminals and measuring the resulting current. Intuitively, it represents the maximum current the network can deliver. Note that option A describes how to find V_th (the Thévenin voltage), and option C describes how to find R_N = R_th. Option D is actually the formula I_N = V_th/R_th, which lets you compute I_N from a known Thévenin equivalent.
Question 2 Multiple Choice
An engineer has two identical Thévenin equivalents (V_th = 12V, R_th = 4Ω each) that she wants to connect in parallel and analyze as a single source. What is the most efficient approach?
AConvert each to its Norton equivalent (I_N = 12/4 = 3A, R_N = 4Ω), add the Norton currents (6A total), and combine the parallel Norton resistances (2Ω combined) — done in two steps
BAdd the Thévenin voltages directly (24V total) and keep the same resistance (4Ω)
CSolve the complete combined circuit from scratch using Kirchhoff's voltage law at each node
DYou cannot combine Thévenin equivalents in parallel — they must be connected in series
This is precisely why Norton equivalents are preferred for parallel combinations. In parallel, Norton current sources add directly (3A + 3A = 6A) and their parallel resistances combine as 4Ω ∥ 4Ω = 2Ω. Attempting this with Thévenin equivalents in parallel requires converting to Norton anyway before you can add them, since voltage sources in parallel with different internal resistances require more careful treatment. Option B is wrong: V_th sources in parallel do not simply add their voltages. The duality principle makes the choice of representation a matter of analytical convenience.
Question 3 True / False
The Norton resistance R_N of a circuit is generally different from the Thévenin resistance R_th of the same circuit, since one is associated with a current source and the other with a voltage source.
TTrue
FFalse
Answer: False
R_N always equals R_th exactly. Both are found by the same method: kill all independent sources (replace voltage sources with shorts, current sources with open circuits) and measure the resistance seen looking into the terminals from outside. This resistance is a property of the network's passive structure alone — it doesn't depend on whether the circuit is being described as a Thévenin or Norton equivalent. The two forms represent the same network in different languages; only the source element (voltage vs. current) changes.
Question 4 True / False
Norton equivalents are more analytically convenient than Thévenin equivalents when combining subcircuits connected in parallel.
TTrue
FFalse
Answer: True
In parallel connections, current sources add directly and parallel resistances combine with the standard formula. This makes Norton equivalents natural for parallel networks: you add Norton currents and combine resistances in parallel, both single-step operations. Thévenin equivalents are natural for series connections, where voltage sources add directly and series resistances simply sum. This is the practical meaning of duality — both representations are correct, but choosing the one that matches the topology makes the algebra significantly cleaner.
Question 5 Short Answer
A circuit has a Thévenin equivalent of V_th = 10V and R_th = 5Ω. Describe the Norton equivalent and explain why R_N must equal R_th.
Think about your answer, then reveal below.
Model answer: The Norton equivalent is I_N = V_th / R_th = 10V / 5Ω = 2A in parallel with R_N = 5Ω. R_N equals R_th because both resistances are found by the identical procedure: kill all independent sources and measure the resistance seen at the terminals from outside. This resistance depends only on the network's passive topology (resistors and the structure of dependent sources, if any) — it is independent of the source type being described. Since Thévenin and Norton are two descriptions of the same physical network, they must share the same terminal resistance. The only difference between the two forms is whether the independent source is represented as a voltage source in series (Thévenin) or a current source in parallel (Norton).
The conversion I_N = V_th / R_th is not a formula to memorize as a separate fact — it follows directly from the requirement that both equivalents produce the same short-circuit current and the same open-circuit voltage. Setting up those two conditions immediately gives I_N = V_th / R_th and R_N = R_th.