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Electricity
Eduqas A Level Physics — Revision Notes
Component 2: Electricity and the Universe · Topics 1–
Conduction of Electricity
Electric current is the flow of charged particles. In metals, these are free electrons. In electrolytes (e.g. salt solutions) and gases, positive and negative ions carry the current.
Current and Charge
Electric current I is defined as the rate of flow of charge:
I =
∆Q
∆t
⇒ Q = It
The SI unit is the ampere (A), defined via the magnetic force between parallel wires. Conventional current flows from + to − outside the cell. Electron flow is the opposite direction (− to +).
Drift Velocity
Free electrons in a metal move randomly at very high speeds, but they drift slowly in one direction when a field is applied. The drift velocity vd is this slow bulk movement:
I = nAvde
where n = number density of charge carriers (m−^3 ), A = cross-sectional area, e = 1. 6 × 10 −^19 C. Typical drift velocities are around 10−^4 m s−^1 — much slower than the signal itself, which travels at close to c.
Resistance
Ohm’s Law and Resistance Resistance is defined as: R =
V
I
(always true)
Ohm’s Law states that for a metallic conductor at constant temperature, V ∝ I (i.e. R is constant). Many components do not obey Ohm’s law.
Resistivity
The resistance of a conductor depends on its material and dimensions:
R =
ρL A
where ρ is the resistivity (units: Ω m), L is length, A is cross-sectional area. A longer, thinner wire has more resistance. Resistivity is a property of the material, not the shape.
I–V Characteristics
Component Characteristic Metallic resistor Straight line through origin (Ohmic) Filament lamp Curve — gradient decreases (resistance increases with temperature) Diode No current in reverse; current rises steeply above ∼0.6 V forward Thermistor (NTC) Resistance decreases as temperature rises LDR Resistance decreases as light intensity increases
DC Circuits
Kirchhoff’s Laws KCL (Current Law): The total current entering any junction equals the total current leaving it. This is just conservation of charge. X Iin =
X
Iout
KVL (Voltage Law): The sum of all EMFs around any closed loop equals the sum of all voltage drops: (^) X E =
X
IR
This is conservation of energy.
Series and Parallel
Series: Same current through all components. Resistances add:
Rtotal = R 1 + R 2 + · · ·
Parallel: Same voltage across all components. Reciprocals add: 1 Rtotal
R 1
R 2
EMF and Internal Resistance
A real battery has an internal resistance r. When current I is drawn:
E = Vterminal + Ir = I(R + r)
The “lost volts” = Ir explains why the terminal voltage drops under load. On an E-vs-I graph, E is the y-intercept and −r is the gradient.
Worked Example: Internal Resistance
A battery of EMF 9 V and internal resistance 2 Ω drives a 7 Ω external resistor. Find current and terminal voltage.
I =
E
R + r
= 1 A
Vterminal = E − Ir = 9 − (1)(2) = 7 V
Summary of Key Equations
Electricity Formula Sheet
Current: I = ∆Q/∆t, I = nAvde Resistance: R = V /I, R = ρL/A Power: P = IV = I^2 R = V 2 /R EMF: E = I(R + r) Potential divider: Vout = VsR 2 /(R 1 + R 2 ) Capacitance: C = Q/V Capacitor energy: W = 12 CV 2
Discharge: Q = Q 0 e−t/RC^ , τ = RC
