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Induction · Paper 2 — Free Physics HL Practice Questions

What this topic covers

Fields is where gravity, electricity and magnetism finally get shown to be the same trick played three times: a source (mass, charge, or moving charge), a field that falls off as $1/ r^{2}$ or sits uniform between plates, and a potential that tells you the energy cost of moving through it. HL bolts on two whole subtopics that SL never sees — motion in combined electric and magnetic fields, and electromagnetic induction — and a huge fraction of the marks in this theme come from just two calculation types: transformer turns ratios and induced emf from $ΔΦ/Δ t$ . Get those automatic, then spend the rest of your revision on the sign conventions ( $V_{g}$ is always negative), the vector-vs-scalar traps ( $g$ vs $V_{g}$ , $E$ vs $V$ ), and the direction rules (Lenz's law, $q v \times B$ ) that separate a 6 from a 7.

Read the full Fields lesson notes →

1ChallengeSAQ-LTransformers and power transmission7 marksPaper 2~11 min

Data

- Resistivity of copper:

\rho_\text{Cu} = 1.7 \times 10^{-8}\,\Omega\,\text{m}

- Resistivity of aluminium:

\rho_\text{Al} = 2.6 \times 10^{-8}\,\Omega\,\text{m}

A remote mining facility in northern Canada is powered by a

50\,\text{Hz}

AC generator that produces

12\,\text{kV}

at the output terminals. The facility is connected to a transformer substation

85\,\text{km}

away via a pair of copper transmission cables, each with a resistance of

0.015\,\Omega\,\text{km}^{-1}

. The substation contains a step-down transformer that reduces the voltage to

240\,\text{V}

for local use. The total power demand of the facility is

5.4\,\text{MW}

at a power factor of

0.95

(lagging). Assume ideal transformer operation and that the transmission line operates at the generator voltage.

(a)

Calculate the current in the transmission cables. [1 mark]

(b)

Calculate the total power dissipated as heat in the transmission cables. [2 marks]

(c)

Explain why the power loss in the cables would be significantly greater if the generator voltage were instead

240\,\text{V}

, without using a step-up transformer. [2 marks]

(d)

The facility manager proposes replacing the copper cables with aluminium cables of identical length and cross-sectional area. Calculate the power loss in the aluminium cables and hence evaluate whether this replacement is advisable, referring to power efficiency, cost, and safety. [2 marks]

Solutions

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