Electricity: Charge, Circuits and Power

Formulas (3)

• Electric charge: carried by particles, quantised and conserved · Charge as a count of elementary charges
  $$Q = n e$$
• Coulomb's law: the force between two point charges · Coulomb's law
  $$F = k\,\frac{q_1 q_2}{r^2}$$
• Electric field: force per unit charge, and field lines · Electric field
  $$E = \frac{F}{q} \qquad E = k\,\frac{Q}{r^2}$$

Reference tables (1)

Watch out for (6)

• A neutral atom has zero charge, not a small one
  → Electric charge: carried by particles, quantised and conserved
• Positive charge means electrons lost, not protons gained
  → Electric charge: carried by particles, quantised and conserved
• Insulators do not share charge on contact
  → Conductors and insulators: where charge can move
• The bigger charge does not feel a bigger force
  → Coulomb's law: the force between two point charges
• Distance enters squared
  → Coulomb's law: the force between two point charges
• Electrons move against the field
  → Electric field: force per unit charge, and field lines

Formulas (2)

• Potential difference, the work W = qV and the electronvolt · Work on a charge, and the uniform field
  $$W = qV \qquad E = \frac{V}{d}$$
• Capacitors: C = Q/V, stored energy, series and parallel · Capacitance, energy and combinations
  $$C = \frac{Q}{V} \qquad U = \tfrac{1}{2}CV^2 \qquad C_{\parallel} = C_1 + C_2 \qquad \frac{1}{C_{\text{series}}} = \frac{1}{C_1} + \frac{1}{C_2}$$

Watch out for (4)

• The electronvolt is energy, not voltage
  → Potential difference, the work W = qV and the electronvolt
• Plate spacing goes in metres
  → Potential difference, the work W = qV and the electronvolt
• Capacitors combine the opposite way to resistors
  → Capacitors: C = Q/V, stored energy, series and parallel
• Stored energy is half QV
  → Capacitors: C = Q/V, stored energy, series and parallel

Formulas (3)

• Electric current: charge per second, and which way it flows · Current
  $$I = \frac{Q}{t}$$
• Resistance and Ohm's law · Ohm's law
  $$V = I R$$
• Resistivity: how a wire's length and thickness set its resistance · Resistance of a wire
  $$R = \frac{\rho L}{A} \qquad A = \frac{\pi d^2}{4}$$

Watch out for (3)

• Electrons move against the conventional current
  → Electric current: charge per second, and which way it flows
• Ohm's law needs a constant resistance
  → Resistance and Ohm's law
• Diameter is squared in the area
  → Resistivity: how a wire's length and thickness set its resistance

Formulas (3)

• Resistors in series and in parallel · Series and parallel
  $$R_{\text{series}} = R_1 + R_2 + \dots \qquad \frac{1}{R_{\parallel}} = \frac{1}{R_1} + \frac{1}{R_2} + \dots$$
• Kirchhoff's rules, the potential divider and meters · Potential divider
  $$V_1 = V \, \frac{R_1}{R_1 + R_2}$$
• EMF and internal resistance of a battery · EMF and internal resistance
  $$\varepsilon = I(R + r) \qquad V = \varepsilon - I r$$

Watch out for (3)

• A parallel total is smaller than every branch
  → Resistors in series and in parallel
• Meters in the wrong place
  → Kirchhoff's rules, the potential divider and meters
• Terminal p.d. is less than the e.m.f. when current flows
  → EMF and internal resistance of a battery

Formulas (2)

• Electrical power: P = VI = I²R = V²/R · Electrical power
  $$P = VI = I^2 R = \frac{V^2}{R}$$
• Electrical energy and the kilowatt-hour · Electrical energy
  $$E = P t = V I t \qquad 1\ \text{kWh} = 3.6 \times 10^6\ \text{J}$$

Reference tables (1)

Watch out for (3)

• Doubling the current quadruples the power
  → Electrical power: P = VI = I²R = V²/R
• The kilowatt-hour is energy, not power
  → Electrical energy and the kilowatt-hour
• Zero resistance does not remove the magnetic effect
  → The three effects of an electric current