Unit 1 Section 3 Conservation of E and C in Circuits

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Conservation of Charge

As charge flows through a circuit, it doesn't get used up or lost.

This means that whatever charge flows into a junction will flow out again.

Since current is rate of flow of charge, it follows that whatever current flows into a junction is the same as the current flowing out of it.

Kirchhoff's first law: The total current entering a junction = the total leaving it.

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Conservation of Energy

In electrical circuits, energy is transferred around the circuit.

Energy transferred to a charge is e.m.f., and energy transferred from a charge is potential difference.

In a 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.

e.m.f. = sigma(IR)  

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Series Circuits

There will be the same current at all points of the circuit, since there are no junctions.

The e.m.f. is split between the components by kirchhoff's second law, so: e.m.f. = V1 + V2 + V3

The voltage splits proportionally to the resistance, as V = IR

V = IR so if I is constant: IR total = IR1 + IR2 + IR3

Cancelling the I's gives: R total = R1 + R2 + R3

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Parallel Circuits

The current is split at each junction, so: I = I1 + I2 + I3

There is the same p.d. across all components - there are seperate loops and within each loop the e.m.f. equals the sum of of the individual p.d.'s. so: V/Rtotal = V/R1 + V/R2 + V/R3

Cancelling the V's gives: 1/Rtotal = 1/R1 + 1/R2 + 1/R3

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Cells in Series

For cells in a series circuit, you can calculate the total e.m.f. of their combination by adding their individual e.m.f.'s.

This make sense if you think about it, because each charge goes through each of the cells and so gains (electrical energy) e.m.f. from each one.

e.m.f. total = e.m.f.1 + e.m.f.2 + e.m.f.3

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Cells in Parallel

For identical cells in a parallel circuit, the total e.m.f. of the combination of cells is the same size as the e.m.f. of each of the individual cells.

This is because the amount of charge flowing in the circuit doesn't increase by adding cells in parallel, but the number of paths the charges can take does.

The current will split equally between identical cells.

The charge only gains e.m.f. from cell it travels through -  so the overall e.m.f. in the circuit doesn't increase. 

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Glossary

Kirchhoff's first law: The total current entering a junction = the total current leaving it.

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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