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B.5.3—Resistance

Syllabus
First assessment 2025
Objective
—
Level
HL

Calculate Resistance from Voltage and Current

Resistance

Resistance is the ratio of potential difference across a component to current through it:

R=VIR=\frac{V}{I}

Its SI unit is the ohm, Ω.

Conductors, insulators and the origin of resistance

A conductor has mobile charge carriers that can drift when an electric field is applied. In a metal these carriers are electrons. In an insulator, charge carriers are not sufficiently mobile for a sustained current under ordinary conditions. Resistance arises because moving carriers interact with the material's lattice and transfer energy to it.

Interpret the ratio

For a given current, a larger potential difference means larger resistance. Resistance describes how strongly a component opposes charge flow under the stated operating conditions.

Worked example from the mapped local textbook

A component carries 0.78 A0.78\,\mathrm{A} when the potential difference across it is 4.4 V4.4\,\mathrm{V}.

R=VI=4.40.78=5.6 ΩR=\frac{V}{I}=\frac{4.4}{0.78}=5.6\,\Omega

This is its resistance at that operating point; it should not be assumed constant unless the component is ohmic under fixed conditions.

Unit check

From R=V/IR=V/I, 1 Ω=1 V A−11\,\Omega=1\,\mathrm{V\,A^{-1}}. Use the voltage across the component, not the emf of the whole source unless they are equal in the circuit.

Common trap

Resistance is not the same as current. A component can have high resistance and a small current for a given voltage.

B.5.3 Exam Analysis

Assessment in practice

1–2 marks
How it is assessed

The evidence asks for a numerical resistance from voltage and power or tests recognition of a valid unit for resistance. Both require identifying the component quantities before calculating or selecting.

Command terms

Calculate / Identify

What earns marks

Use the resistance relationship in the form that matches the data: R=V/I, or R=V²/P when voltage and power are supplied. Show the substitution and give resistance in ohms; check that the selected voltage is the potential difference across the component.

Watch for

Using P/V or P/I as resistance without checking which power equation is being rearranged.

Representative question

Question 1

[Maximum number: 1]

What is a possible unit of electrical resistance?

A

WA−2\mathrm{WA}^{-2}

B

AV−1\mathrm{AV}^{-1}

C

VW−2\mathrm{VW}^{-2}

D

WV−2\mathrm{WV}^{-2}

Retrieve the B.5 Current and Circuits Model

Source and transfer

Cells provide emf arepsilonarepsilon, the energy transferred per unit charge by the source. Electrical energy transferred in a circuit is E=VItE=VIt, and power is P=VI=I2R=V2/RP=VI=I^2R=V^2/R. Keep emf, terminal potential difference, energy and power distinct.

Current and circuit laws

Conventional current is the direction positive charge would move, with I=Δq/ΔtI=\Delta q/\Delta t. In DC, the direction is constant; in AC, it reverses periodically. Apply Kirchhoff’s junction rule to charge conservation and the loop rule to energy conservation.

Resistance model

Use R=V/IR=V/I for a component, R=hoL/AR= ho L/A for a uniform conductor, and the correct series or parallel combination rule. Ohmic behaviour means constant resistance at constant physical conditions; non-ohmic behaviour requires reading the gradient or ratio from the graph at the stated point.

Real and variable components

For a real cell, arepsilon=I(R+r)arepsilon=I(R+r) and V= arepsilon-Ir. A variable resistor changes circuit resistance; LDRs and thermistors use a stimulus-dependent resistance. Before calculating, draw or inspect the circuit, identify the fixed quantity, and state the relevant assumption.

Explore Ohm's Law by Changing Voltage and Resistance