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A-LEVEL 9702 · AS · TOPIC 10
D.C. circuits
The build-chain of the topic: a real source has e.m.f. and internal resistance, two conservation laws (Kirchhoff's) govern every junction and loop, those laws give the rules for combining resistance, and one common arrangement, the potential divider, sets an output voltage. Around the hexagon are the four ideas; above is what it builds on, below is where it leads.
TOPIC 10: D.C. CIRCUITS
CAMBRIDGE A-LEVEL PHYSICS 9702 · PATHWAYS
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BUILDS ON
T9 Electricity: I, V, R, P = VI, V = IR T5 Energy: conservation of energy 10.1
10.2
10.2
10.3
TOPIC 10
D.C.
CIRCUITS
1 · PRACTICAL CIRCUITS & E.M.F.
A real cell is not a perfect source.
E.m.f. E is the energy given per unit charge: E = W / Q
Internal resistance r wastes ‘lost volts’ I r inside
Terminal p.d. V falls below E once current flows
V = E − I r
E = V only when I = 0
E
r
R
I
terminal p.d. V
source = e.m.f. E in series with r
2 · KIRCHHOFF’S LAWS
Two conservation laws rule every circuit.
First law (charge): current into a junction equals
current out of it. Charge is conserved.
Second law (energy): around any loop the sum of
e.m.f.s equals the sum of p.d.s. Energy is conserved.
Σ I(in) = Σ I(out)
Σ E = Σ I R (round a loop)
I₁
I₂
I₃
I₁ = I₂ + I₃ at the junction
charge in = charge out per second
3 · COMBINING RESISTANCES
The laws give the rules for adding resistors.
Series: same current, p.d.s add (second law)
Parallel: same p.d., currents add (first law)
Series total is larger; parallel total is smaller
series: R = R₁ + R₂
parallel: 1/R = 1/R₁ + 1/R₂
series
R₁
R₂
parallel
R₁
R₂
4 · POTENTIAL DIVIDERS
Split a voltage in the ratio of resistances.
Two series resistors share the supply by ratio
Swap R₂ for a thermistor or LDR to sense and switch
A potentiometer compares p.d.s by a null method:
balance when the galvanometer reads zero, no current
V(out) = R₂ / (R₁ + R₂) × V(in)
V(in)
R₁
V(out)
R₂
output tapped between R₁ and R₂
LEADS TO
T18 Electric fields: potential difference and E = V/d T19 Capacitance: charging and R-C circuits T21 A.C.: circuits with changing current Each reuses one idea: e.m.f., p.d. and the two Kirchhoff laws stay true once charge can store, vary or alternate.
← Builds on IGCSE: Electric circuits