B.5 Current and circuitsIB Physics SL: Revision notes
Section 1
Cells, emf and circuits
A cell is a source of emf (ε): the energy transferred to each coulomb of charge by the source. Chemical cells convert chemical energy to electrical energy; solar (photovoltaic) cells convert the energy of light. Circuit diagrams represent components with standard symbols; you may be asked to describe an arrangement in words.
Real cells have internal resistance r, so part of the emf is 'lost' inside the cell:
ε = I(R + r), so the terminal pd is V = ε − Ir.
Two readings of V and I at different loads give two equations ε = V + Ir: solve them simultaneously for ε and r.
Section 2
Current and potential difference
Current is the rate of flow of charge carriers: I = Δq/Δt (1 A = 1 C s⁻¹). In metals the carriers are free electrons; conventional current is taken as the direction of positive charge flow.
Potential difference V is the work done per unit charge in moving a positive charge between two points: V = W/q (1 V = 1 J C⁻¹).
Conductors contain many mobile charge carriers; insulators have very few, because their electrons are bound to atoms.
Section 3
Resistance, resistivity and Ohm's law
Resistance is defined as R = V/I. It arises because moving charge carriers collide with the vibrating lattice ions, transferring energy to them.
Resistivity ρ is a property of the material: ρ = RA/L, so R = ρL/A (unit Ω m).
Ohm's law: the current in a conductor is proportional to the pd across it, provided temperature and other physical conditions are constant. An ohmic conductor has constant resistance; a non-ohmic conductor does not.
A filament lamp is non-ohmic: a larger current heats the filament, the lattice ions vibrate more, collisions increase and the resistance rises. This heating effect is present in all resistors carrying current.
Saying a component is ohmic because R = V/I works for it. R = V/I defines resistance for any component; it is ohmic only if that ratio stays constant.
Section 4
Electrical power
The power dissipated in a resistor is
P = IV = I²R = V²/R
Choose the form that uses the quantity that is the same for the components you are comparing: I²R for series components (same current), V²/R for parallel components (same pd).
Section 5
Series and parallel combinations
Series: same current through each; pds add: V = V₁ + V₂ + …; R_s = R₁ + R₂ + …
Parallel: same pd across each; currents add: I = I₁ + I₂ + …; 1/R_p = 1/R₁ + 1/R₂ + …
The combined parallel resistance is always less than the smallest individual resistance.
When a non-ohmic component is in a circuit, use its own V–I data at the actual current or pd, not a resistance measured under other conditions.
Section 6
Variable resistors
A variable resistor (rheostat) controls the current in a circuit. Used as a potential divider, a resistor with a sliding contact gives an adjustable output pd. Some resistors change their resistance with conditions: the resistance of a light-dependent resistor (LDR) falls as light intensity rises, and that of a common thermistor (NTC) falls as temperature rises. These are used in sensing circuits.
That's the notes covered.
Carry on to the next subtopic.