Conservation of Energy & Charge in Circuits


Charge doesn’t ‘leak away’ - it’s conserved

Charge flows - doesn’t get used up or lost.
Whatever charge flows into a junction will flow out again.
Current = rate of flow of charge, it follows that whatever current flows into a junction = same as current flowing out.
Kirchhoff’s first Law - The total current entering a junction = the total current leaving it.

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Energy is conserved too

Energy is conserved.
Electrical circuits - energy is transferred round circuit.
Energy transferred to a charge = e.m.f, energy transferred from a charge = p.d
Closed loop - these two quantities must be equal if energy is conserved.
Kirchhoff’s second law - The total e.m.f around a series circuit = the sum of the p.d.s across each component.

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Exam questions might get you to combine resistors

Series circuit:
1. Same current at all points of circuit (as there are no junctions)
2. E.m.f split between components (Kirchoff’s second law) so: ε = V1 + V2 + V3
3. V = IR, so if I is constant: IR total = IR1 + IR2 +IR3
4. Cancelling the Is gives: R total = R1 + R2 + R3
5. As R = 1/G, you can write this in terms of conductance: 1/G total = 1/G1 + 1/G2 + 1/G3
Parallel circuits:
1. Current is split at each junction so:cI = I1 + I2 + I3
2. Same p.d across all components (three separate loops-within each loop e.m.f = sum of individual p.d.s)
3. So V/R total = V/R1 + V/R2 + V/R3
4. Cancelling the Vs gives: 1/R total = 1/R1 + 1/R2 + 1/R3
5. As R = 1/G, you can write this in terms of conductance: G total = G1 + G2 + G3

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