DSE Physics: electricity and circuits (tutor lesson plan)

2026-11-03

Tutor lesson-prep guides · Secondary Physics

Students know V equals IR until a parallel branch appears. This lesson teaches two moves only: draw the equivalent circuit, then place the numbers segment by segment.

Objectives — Students can: (1) reduce a series and parallel network to one equivalent resistance (6 ohm parallel with 3 ohm gives 2 ohm, plus 4 ohm in series gives 6 ohm); (2) find the main current from the supply and then the voltage and power of each segment (12 V gives 2 A and 16 W in the 4 ohm resistor); (3) compute energy cost with P = VI and kWh, and explain why internal resistance makes the terminal voltage lower than the emf.

01 Prerequisites (3-minute check)

If any of these fails, fix it before the lesson starts.

Skill	Quick check	Pass mark
Ohm law	The units in V = IR	V, A, ohm
Reciprocals	What 1/6 plus 1/3 equals	1/2
Power	When to use P = VI and P = I squared R	Use the second when I and R are known

02 Lesson flow (45 minutes)

Time	Stage	Tutor does	Student does
0-8 min	Draw the equivalent circuit	Reduce 6 ohm parallel with 3 ohm to 2 ohm	Student draws both stages
8-20 min	Place the numbers	Total becomes 6 ohm, so 12 V drives 2 A	Teacher gives the order, student fills the numbers
20-32 min	Power and energy	16 W in the 4 ohm resistor; 1.5 kW for 2.5 h is 3.75 kWh	Both units correct
32-40 min	Internal resistance	With r = 0.5 ohm the terminal voltage is 11 V, not 12 V	Say “emf unchanged, terminal voltage drops”
40-45 min	Exit check	Mark on the spot, correct on the spot	Three out of three

03 Teaching script (read it out)

Scene 1: Reduce first, substitute later

Six ohms in parallel with three: 1/R = 1/6 + 1/3 = 1/2, so the equivalent is 2 ohm, smaller than either branch. In series with 4 ohm the total is 6 ohm. With a 12 V supply the main current is I = V/R = 12/6 = 2 A.
The parallel section carries I times 2, which is 4 V, and the 4 ohm resistor takes 8 V; the two add to 12 V, which is the check. Power in the 4 ohm resistor is I squared R, 2 squared times 4, which is 16 W, and V times I gives the same.
The order is always three sentences: which two are in parallel, which two are in series, and only then the numbers. Students substitute too early because nobody made them draw first.

Ask the student: why must the equivalent of a parallel pair be smaller than 3 ohm?

Scene 2: Power is the rate, energy is the total bought

Power is the rate of energy transfer, in watts, which is joules per second. One resistor has three versions: P = VI, P = I squared R and P = V squared over R. Use I squared R when current and resistance are known, V squared over R when voltage and resistance are known, and VI when both are to hand. A wrong choice rarely changes the answer but always adds a step.
Energy is power times time, and household billing uses kWh: a 1.5 kW heater for 2.5 hours uses 3.75 kWh, and at 1.2 dollars per unit that costs 4.50 dollars. Drill kW times hours rather than W times seconds, because the bill is in kWh.
Marks are usually lost on units, not formulas: mixing W with kW, or leaving minutes as minutes.

Ask the student: why is 1.5 kW for 2.5 hours not 3.75 W?

Scene 3: Internal resistance: emf stays, terminal voltage falls

A real cell has internal resistance r. With an emf of 12 V, r = 0.5 ohm and an external 6 ohm, the total is 6.5 ohm, so the current is 12/6.5 which is about 1.8 A, and the terminal voltage is emf minus Ir, 12 minus 2 times 0.5, which is 11 V.
Two sentences carry the concept: the emf is the energy per unit charge gained inside the cell, and the terminal voltage is what the external circuit actually receives. The larger the current, the more the internal resistance takes, so the terminal voltage falls, which is why headlights dim when the starter motor runs.
In calculation, find the current from the total resistance including r, then work back to the terminal voltage. Dividing 12 V by the external resistance alone is the classic error.

Ask the student: why does the terminal voltage fall when more appliances are connected and the total resistance drops?

04 Question types and worked steps

Type	Example	Steps	Answer
Equivalent resistance	What is the equivalent of 6 ohm in parallel with 3 ohm?	Add reciprocals, then invert	2 ohm
Current and voltage sharing	A 12 V supply across 2 ohm in series with 4 ohm; find each voltage	Total resistance, main current, then multiply each segment	4 V and 8 V
Power	The 4 ohm resistor carries 2 A; find the power	Use I squared R and state the unit	16 W
Energy cost	1.5 kW for 2.5 hours at 1.2 per unit; find the cost	Find kWh first, then multiply by the tariff	3.75 kWh, 4.50 dollars

Sanity check (teach this): Check the numbers: 1/6 plus 1/3 is 1/2, so 2 ohm; plus 4 ohm gives 6 ohm; 12 V divided by 6 ohm is 2 A; 2 A times 2 ohm is 4 V and 2 A times 4 ohm is 8 V, which sum to 12 V; I squared R is 16 W; with r = 0.5 ohm the current is 1.8 A and the terminal voltage 11 V; 1.5 kW for 2.5 hours is 3.75 kWh and costs 4.50. Every result can be checked from another direction.

05 Independent practice (3 questions)

Question	Answer	What to watch
What is the equivalent of 12 ohm in parallel with 4 ohm?	3 ohm	Whether reciprocals are added rather than resistances
That network is connected to 6 V; find the main current	2 A, since the total is 3 ohm	Whether reduction happens before dividing the voltage
A 2 kW air conditioner runs for 4 hours at 1.2 per unit; find the cost	8 kWh, 9.60 dollars	Whether kW is multiplied by hours before the tariff

06 Common mistakes and what to say

Mistake	Student writes	Say this
Adding parallel resistances	“6 ohm parallel with 3 ohm is 9 ohm”	“A parallel equivalent is always smaller than the smallest branch; add reciprocals.”
Dividing emf by the external resistance	“12 V over 6 ohm is 2 A” when r is present	“With internal resistance, use the total resistance, external plus internal.”
Wrong power version	Using V squared over R when only I and R are known	“If you have no V, use I squared R first.”
Mixing kW and W	“1.5 kW for 2.5 hours is 3.75 W”	“kW times hours gives kWh, which is the unit on the bill, not watts.”

07 Homework (paper, section and question numbers)

DSE physics electricity paper — Circuit questions 1 to 4: draw the equivalent circuit, then write total resistance and main current, in 20 minutes.
Energy section of the same paper — Questions 5 to 7, including one cost question and one internal resistance question; state units and verify that segment voltages sum to the supply.

08 Exit check (last 5 minutes)

Question	Answer	Decision
Equivalent of 6 ohm parallel with 3 ohm	2 ohm	Answering 9 ohm means parallel is still treated as series
Main current from 12 V across 6 ohm	2 A	Answering 1 A means 12 ohm was used or the reciprocal was misread
Energy of 1.5 kW for 2.5 hours	3.75 kWh	Answering 3.75 W means power and energy are confused

09 Tutor FAQ

Must the reciprocal formula always be used?

Two resistors can use the product over sum form; three or more are safer with reciprocals.

Does DSE examine internal resistance?

Yes, usually as the difference between emf and terminal voltage, solved by using total resistance first.

Must cost questions use kWh?

Yes. Hong Kong bills in units of kWh; watts times seconds gives joules and needs another conversion.

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A TutorZone lesson-prep guide. Written by the TutorZone team; questions and lesson flow are original and are not taken from any school or publisher material.