Exam prep

AP Physics C E and M Unit 11: two rules, one differential equation

Unit 11 runs on two conservation statements dressed as rules. Charge does not pile up at junctions, and energy gained around any loop is spent by the end of it. Everything else is bookkeeping, until a capacitor joins and turns the loop rule into a differential equation solved by an exponential.

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Upload your PDF, photograph your notebook, or point the camera. WeSolve+ writes questions from that material, explains why each answer is right, reads the chapter back to you as a podcast, and remembers every item you missed until you own it.

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The tool below is a small browser-only tool and it is not WeSolve+: paste a few lines and text rules turn them into cards on the spot. The real app, the one that uses AI, is behind the link above.

Unit 11 circuit rules, from your own notes

This is a browser-only tool, and that is all it isIt splits the text you paste by rule, and nothing else. WeSolve+ is a different thing entirely: it reads your whole PDF with AI, writes the reasoning behind every question, speaks the chapter back to you, and remembers what you missed so it can return it. Try the real app now, free!

Cards come out of the rules applied to your paste. The tool never saw the lecture, so it can only be as complete as the text you gave it.

Kirchhoff's rules are conservation laws in disguise

The junction rule is charge conservation, the loop rule is energy conservation per unit charge, and Kirchhoff's laws together solve any resistor network patience allows. Sign discipline decides everything: pick loop directions, mark battery gains and resistor drops, and let a negative answer simply mean the guessed direction was backwards.

Real batteries sag, and the exam measures the sag

A battery's terminal voltage is its emf minus the current times internal resistance, so the harder a circuit draws, the less the terminals deliver. Graph prompts plot terminal voltage against current and read emf from the intercept and internal resistance from the slope. That one line of algebra is a recurring lab question in this unit.

Capacitors bend time, and the limits are free answers

At the first instant an uncharged capacitor accepts current like a plain wire; fully charged, it blocks like a break. Those two limiting circuits need no calculus and answer the first parts of most RC circuit questions. Reasoning the limits before touching the exponential is the reliable order of operations.

The RC equation is a differential equation, and C wants the derivation

Write the loop rule with the capacitor's charge in it, and a first order differential equation appears whose solution rises like one minus an exponential with time constant RC. The free response asks for that construction, separation of variables shown, rather than the memorised result. Rehearse the derivation until it is a procedure, then the answer is bonus.

The time constant is a unit of story, so read graphs in RC

After one time constant the charging gap has shrunk by the factor e; after a few, the circuit is effectively settled. Questions hand you a curve and ask for RC from a tangent, an intercept or a fraction reached. Marking the axis in multiples of RC turns every such graph into the same graph, which is the point.

What to photograph for Electric Circuits

Your loop equations and RC derivations. Related: Unit 10, photo to quiz and pricing.

Sources used on this page

Regimes of the same circuit
MomentCapacitor acts likeWhat to compute
Switch just closedA plain wireCurrents by resistor rules
Long after closingAn open breakFinal charges, zero branch current
In betweenThe exponential regimeq of t with constant RC
DischargingA fading sourceDecay by e to the minus t over RC
Terminal voltage sagsInternal resistance at workEmf minus I times r
Two branches at a nodeJunction rule territoryCurrents in equals currents out

What does AP Physics C E and M Unit 11 cover?

Kirchhoff's rules, series and parallel networks, internal resistance, power, and RC circuits treated with calculus.

How do I handle a capacitor at t equals zero?

An uncharged capacitor behaves like a wire at the first instant and like a break when fully charged. The two limits answer most first parts.

What is the time constant of an RC circuit?

The product RC: the time for the charging gap to shrink by the factor e. A few time constants settle the circuit.

What does internal resistance do to a battery?

It lowers terminal voltage as current rises: terminals deliver emf minus I times r, which is why the exam plots voltage against current.

Why do my loop equations give a negative current?

The guessed direction was backwards. The magnitude stands, and the sign is information rather than an error.

Can I build questions from my own Unit 11 notes?

Yes. The questions follow the upload: photograph these pages or attach the PDF, and nothing outside them enters the set.

Last updated: 2026-08-15