Predict what opening one branch changes elsewhere

Establish the model and evidence

Series and parallel describe electrical connections, not how components happen to look on a page. Elements are in series only when the same charge has no alternative path between them. Parallel branches connect the same pair of nodes and therefore share a voltage difference. A shared upstream resistor carries the sum of branch currents, not the current of either branch alone.

The activity connects R0=20 Ω in series with a node that splits into A=60 Ω and a switched branch B. Reduce the parallel pair first: 1/Rp=1/RA+1/RB. Then the source sees R0+Rp. After finding total current, calculate the shared branch voltage and use it separately for each branch current. Check the junction sum instead of assuming equal division.

Opening B removes one path but leaves A connected. Equivalent resistance increases and source current falls. Because the upstream R0 voltage drop is now smaller, the surviving branch A receives a larger voltage and can dissipate more power. This nonlocal change is why the shortcut “removing a branch dims everything” fails. Ideal fixed-voltage sources and fixed resistances are essential assumptions.

The node-potential plot follows one complete loop and returns to its starting potential. The junction rule expresses conservation of charge; the loop rule expresses conservation of energy per charge. Power is a qualitative brightness proxy only when comparing suitable bulbs, and this model does not treat a real filament’s changing resistance or optical efficiency. An open branch is not a short circuit: a short provides a low-resistance alternative rather than removing a path.

Worked evidence

With B=40 Ω closed, Rp=24 Ω and total resistance 44 Ω. Source current is 0.13636 A, branch voltage 3.27273 V, IA=0.05455 A and IB=0.08182 A. Opening B gives total resistance 80 Ω and IA=0.075 A: A’s current rises although total source current falls.

Predict and investigate

Will opening B raise or lower the power of the still-connected A branch?

Retain B=40 Ω closed and open. Reconstruct both current sums and complete source-power versus resistor-power balances. Draw the two node connections before interpreting the potential graph.

Transfer to changed conditions

A 12 V source drives 10 Ω in series with two parallel 30 Ω branches. Find total current and each branch current; then open one branch.

Compare the worked transfer

Initially Rp=15 Ω, total current=0.48 A and each branch current=0.24 A. With one branch open, total resistance=40 Ω and the surviving current=0.30 A. Its power rises from 1.728 W to 2.70 W.

Explain the boundary

Explain why charges are not used up in R0 and why A and R0 do not share current when B is closed.

Read schematic symbols before reducing nodes

The diagram below is a symbol key, not a connected circuit or an instruction to wire equipment. A cell uses unequal parallel lines, a capacitor equal separated plates, a resistor a zigzag (a rectangle is another convention), an open switch a separated lever, and meters circles marked A or V. A diagonal arrow across a resistor symbol denotes an adjustable resistor, not a current direction. A junction dot identifies a connection; merely crossing lines need not connect.

Draw, predict and check: redraw the lesson’s 20 Ω upstream resistor and two branches using these symbols and junction dots. Mark that upstream element as belonging to either closed loop through A or B. Opening B leaves the A loop closed; replacing B by an ideal zero-resistance path instead makes both ends of A the same node, so A has zero voltage. In that virtual shorted-branch limit, the 6 V source still sees the 20 Ω upstream resistor and current is 0.30 A. Do not extend this ideal limit to a bare real source: finite wire and internal resistance then cannot be neglected, and physical shorting is not requested. (Current clauses 11.2.A and 11.5.B.)

Sources and authorship

Physical relationship reference. Current AP Physics 2 framework, checked 30 October 2026. Original cases and computed/synthetic evidence, not actual laboratory measurements. These activities are virtual only: do not reproduce wiring, short-circuit, battery charging, heating or charged-capacitor experiments. Any real practical work requires qualified supervision and an independently approved safety procedure.

Clause-level source/action reconciliation checked 31 October 2026 against the linked current framework and Fall 2026 clarification. Added packets are original virtual comparisons; no new practical or learner-completion claim.