AMME1705 · Introduction to Electromechanical Systems
Circuit Analysis: Kirchhoff & Thevenin
Circuit Analysis: Kirchhoff & Thevenin is the Week 10 topic of AMME1705 Introduction to Electromechanical Systems at the University of Sydney, where two conservation laws unlock any resistor network: Kirchhoff's current law (KCL) — currents into a node sum to zero — and Kirchhoff's voltage law (KVL) — voltage drops round a loop sum to zero. From these you build node and mesh analysis and, above all, the Thevenin equivalent: any two-terminal box of sources and resistors collapses to a single source Vth in series with a single resistance Rth.
It is a compact, almost entirely numeric part of the unit, and it feeds directly into the paper-based final exam, which is worth 33% of the course.
What this chapter covers
- 01State Kirchhoff's current law (KCL): the signed currents into any node sum to zero (∑ I = 0)
- 02State Kirchhoff's voltage law (KVL): the voltage rises and drops round any closed loop sum to zero (∑ V = 0)
- 03Reduce a network first: resistors in series R_eq = R1 + R2 + …, in parallel 1/R_eq = 1/R1 + 1/R2 + …
- 04Read a voltage divider directly: V_out = V_in · R2/(R1 + R2), and know it only holds under negligible load
- 05Solve a one-node circuit by KCL, then recover every branch current from Ohm's law with the correct sign
- 06Find the Thevenin voltage V_th as the open-circuit voltage at the terminals (load removed)
- 07Find the Thevenin resistance R_th by deactivating every independent source — voltage source → short, current source → open
- 08Combine a two-source divider into its equivalent V_th = (V1·R2 + V2·R1)/(R1 + R2), R_th = R1 ∥ R2
- 09Use the equivalent to predict any load: I_L = V_th/(R_th + R_L) and V_L = I_L·R_L
Thevenin equivalent of a two-supply divider, then a load current
- +1(a) With A–B open no terminal current flows, so V_th is just the node voltage at A. KCL at A (currents in mA when V is in volts and R in kΩ): (15 − V_A)/3 + (5 − V_A)/6 = 0.
- +1Multiply through by 6: 2(15 − V_A) + (5 − V_A) = 0 ⇒ 35 − 3V_A = 0 ⇒ V_A = 35/3 = 11.67 V. (Same as the two-source divider formula V_th = (V1·R2 + V2·R1)/(R1 + R2) = (15·6 + 5·3)/(3 + 6) = 105/9 = 11.67 V.)
- +1(b) For R_th, deactivate both independent sources: replace each ideal voltage source by a short (0 V). Now R1 and R2 both run from A to the common ground, so they are in parallel.
- +1R_th = R1 ∥ R2 = (3·6)/(3 + 6) = 18/9 = 2.0 kΩ.
- +1(c) The equivalent is V_th in series with R_th driving R_L, so I_L = V_th/(R_th + R_L) = 11.67/(2.0 + 2.0) kΩ = 11.67/4.0 = 2.92 mA.
- +1Load voltage: V_L = I_L·R_L = 2.92 mA × 2 kΩ = 5.83 V (check: V_th·R_L/(R_th + R_L) = 11.67·2/4 = 5.83 V). The open-circuit 11.67 V sags to 5.83 V once the 2 kΩ load draws current.
Key terms
- Node
- Any junction in a circuit where two or more components meet and share the same voltage. KCL is written at nodes; you count every node, including the ground / reference (0 V) node.
- Loop (mesh)
- Any closed path traced round the circuit and back to the start. KVL is written round loops; mesh analysis uses one equation per independent loop.
- Kirchhoff's current law (KCL)
- Charge is conserved, so the signed currents flowing into any node sum to zero (∑ I = 0), i.e. total current in equals total current out. Currents are in amperes (A).
- Kirchhoff's voltage law (KVL)
- Energy is conserved, so the voltage rises and drops round any closed loop sum to zero (∑ V = 0), i.e. the source voltage equals the sum of the resistor drops. Voltages are in volts (V).
- Voltage divider
- Two series resistors across a supply split the voltage in proportion; with R1 on top and R2 on the bottom, V_out = V_in · R2/(R1 + R2), measured to ground in volts (V). It holds only when negligible current is drawn from the node.
- Thevenin voltage (V_th)
- The open-circuit voltage measured across the terminals of a two-terminal network with the load removed, in volts (V). It is the source in the Thevenin equivalent.
- Thevenin resistance (R_th)
- The resistance looking back into the terminals with every independent source deactivated (voltage source → short, current source → open), in ohms (Ω). It is the series resistance in the Thevenin equivalent.
- Source deactivation
- The step that isolates a network's resistance: replace each ideal voltage source by a short circuit (0 V) and each ideal current source by an open circuit (0 A), then reduce by series/parallel to get R_th.
Circuit Analysis: Kirchhoff & Thevenin FAQ
Do I short a voltage source or open it when finding R_th?
You short it. To find the Thevenin resistance R_th you deactivate every independent source: an ideal voltage source is replaced by a short circuit (a plain wire, 0 V), and an ideal current source is replaced by an open circuit (a gap, 0 A). Then you find the resistance looking back into the terminals by series/parallel reduction. Getting this backwards — opening a voltage source or shorting a current source — is the single most common way students lose the R_th mark, and it corrupts every load calculation that uses R_th afterwards.
What is the difference between KCL/KVL and the Thevenin equivalent?
KCL and KVL are the two fundamental conservation laws — currents into a node sum to zero, and voltages round a loop sum to zero — and you use them to solve for the voltages and currents inside a circuit. The Thevenin equivalent is a result built from those laws: it lets you replace an entire two-terminal network, however complicated, by a single source V_th in series with a single resistance R_th, so that anything you connect to the terminals behaves identically. In short, KCL/KVL solve the circuit; Thevenin repackages it so a changing load becomes a one-line calculation.
Can AI help me with circuit analysis (Kirchhoff & Thevenin) in AMME1705?
Yes — for understanding, not for doing your assessed work for you. Sia can explain step by step how KCL and KVL are set up, why a voltage source shorts and a current source opens when you find R_th, or how a two-source divider collapses to V_th and R_th, and it can walk you through practice problems using your own numbers so you can check your method and sign conventions. It will not hand you answers to a graded quiz, lab or exam, and it cannot promise any particular mark or grade. Use it to build intuition and verify your working, then confirm all assessment rules on your current Canvas.
Studying with AI? Sia — free AI electrical engineering tutor works through AMME1705 step by step.
Exam move
Treat this as a method-and-convention topic: most marks come from setting up KCL/KVL cleanly, deactivating sources the right way, and keeping signs straight. Put the core relations on your one A4 note sheet — series R_eq = R1 + R2 + …, parallel R_eq = R1R2/(R1 + R2), the divider V_out = V_in·R2/(R1 + R2), and the Thevenin recipe (V_th = open-circuit voltage; R_th with voltage sources shorted and current sources opened; then I_L = V_th/(R_th + R_L)). Drill a few one-node KCL problems and a couple of Thevenin reductions with your own numbers until the setup is automatic, and always run the ∑ I = 0 check on your branch currents. Because the final exam demands specified precision (for example to the nearest 0.1 V or 0.01 mA), practise rounding cleanly and pacing at about 1.5 minutes per mark, and confirm the exact exam conditions and permitted materials on your current Canvas.
