Resistors & Resistance — Quick Revision

Mr Toogood's Physics · Electricity basics

AQA 3.5.1.2 & 3.5.1.4
R = V/I
Resistance
I ∝ V
Ohm's law
R_T=R₁+R₂+…
Series
1/R_T=Σ1/R
Parallel

Ohm's law & I–V graphs

Ohm's law: current through a conductor is directly proportional to p.d. across it, at constant temperature. Resistance R = V/I is the inverse of the gradient of an I–V graph.

I-V characteristic graphs for resistor, filament bulb and diode

I–V characteristics: resistor, filament bulb, diode.

  • Resistor (ohmic): straight line through the origin — constant R.
  • Filament bulb: curves as p.d. increases — heats up, R rises (non-ohmic).
  • Diode: ~zero current when reverse-biased; near-vertical rise once forward threshold voltage is reached.

Resistance & temperature

Heating increases particle vibration → more electron collisions → shorter mean free path → higher resistance. This is why a filament bulb's current spikes on switch-on then settles as it heats (negative feedback), producing the S-shaped I–V curve.

Series & parallel resistors

Series: same current throughout; p.d.s add. From Kirchhoff's 2nd law, ε = V₁+V₂+… gives:

R_T = R₁ + R₂ + R₃ + ⋯
Current splitting at a junction in a parallel circuit

Current splits at a junction; each branch shares the same p.d.

Parallel: same p.d. across every branch; currents add (Kirchhoff's 1st law), giving:

1/R_T = 1/R₁ + 1/R₂ + ⋯
Check: R_T for a parallel network is always less than the smallest individual resistor — more paths, less overall opposition to current.
Combining series and parallel resistors in one circuit

Combined circuit: reduce branch-by-branch, working back to the cell.

Exam essentials

Combining rule (4 steps)

  • 1. Start at the branch furthest from the cell.
  • 2. Add series resistors on that branch.
  • 3. Combine the resulting parallel network.
  • 4. Add the result to any remaining series resistors.

Series vs parallel

  • Series: same I everywhere; V splits between components.
  • Parallel: same V across each branch; I splits between branches.

Common slips

  • Don't forget to take the reciprocal as the final step for parallel R_T.
  • Keep full calculator precision between steps — only round the final answer.
  • Ideal ammeter = 0 Ω; ideal voltmeter = ∞ Ω (unless stated otherwise).