How we got there
Read this like a teacher at the board. We go slowly, name every number, and say why we take each step.
Explain in another language · 11
1. What is the question asking?
Read the question twice. Circle the unknown. Underline every number and unit. The paper is asking: A battery (emf 12 V, internal resistance 1.0 Ω) is connected to a 3.0 Ω resistor in series with a parallel pair of 4 Ω and 4 Ω. Find the current from the battery, the terminal potential difference and the potential difference across the parallel pair.
In other words — as if you have never seen this before
If you have never seen this before: Reduce the external circuit to one resistance, use ε = I(R + r) for the current, then V = IR for each part. We will name a method in words, write the formula with no numbers, then substitute one line at a time.
2. What do we already know?
ε=12 V, r=1.0 Ω, R₁=3.0 Ω, R₂=4 Ω ∥ R₃=4 Ω.
3. Which method — and why this one?
Reduce the external circuit to one resistance, use ε = I(R + r) for the current, then V = IR for each part.
4. Step-by-step working
01 / 06
Parallel pair
Rp=(4 × 4)(4 + 4)=2.00 Ω; Rext=3.0+2.00=5.00 Ω.
Rext=5.00 ΩWhy this step: We only do one job per line so a marker can follow the marks — and so you can find a slip without starting over.
02 / 06
Current
I=ε(Rext + r)=12(5.00 + 1.0)=2.00 A.
I=2.00 AWhy this step: We only do one job per line so a marker can follow the marks — and so you can find a slip without starting over.
03 / 06
Potential differences
Vterminal=IRext=2.00×5.00=10.0 V; Vp=2.00×2.00=4.00 V.
V=10.0 V, Vp=4.00 VWhy this step: We only do one job per line so a marker can follow the marks — and so you can find a slip without starting over.
04 / 06
Step G — Sense-check the size
Ask: is this the kind of number a Grade 10–12 paper would want? A speed of 3 000 ms for a learner walking, or a probability bigger than 1, means a unit or algebra slip. Estimate first: round the numbers and do the sum in your head.
Why this step: Markers write ‘unrealistic’ in the margin when the method is right but the size is wild. A 10-second head check often finds a missing 10² or a unit that never changed.
05 / 06
Step F — Box the answer with its unit
I = 2.00 A; V_terminal = 10.0 V; V_parallel = 4.00 V
Why this step: A number without a unit is half a mark on a Physics paper, and a marker can miss a Maths answer that is buried in working.
06 / 06
Step H — What the marker is looking for
On an NSC memo you usually earn: (1) a method mark for naming the right formula or idea in words, (2) an accuracy mark for substituting the given numbers with units, (3) an accuracy mark for the boxed answer with its unit. Write those three lines even if you are unsure of the arithmetic — blank pages score zero.
Why this step: First-timers chase the final number and leave the method blank. The memo still pays out for the idea and the substitution even when the last line is wrong.
5. The answer
I = 2.00 A; V_terminal = 10.0 V; V_parallel = 4.00 V
Copy onto your answer sheet — in this order
Formula: Rext=5.00 Ω
Answer: I = 2.00 A; V_terminal = 10.0 V; V_parallel = 4.00 V
6. Check it like a marker
Leaving out r makes the current too big. The terminal p.d. is always less than the emf while current flows.
7. A trap first-timers fall into
First-timers often grab the first formula they remember, mix units (cm with m, minutes with seconds), or drop a minus sign. Write the formula in words first: “this equals that, because…”