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Resistance and Circuits Paper 3: Challenge
Resistance and Circuits Paper 3: Challenge
Three or more parallel branches, mixed circuits and their voltage division, efficiency and running cost, changed wire length, and the split between rated and actual values.
Direct answers Answers and explanations for all ten questions
01 Paper details (check answers afterwards)
| Item | Detail |
|---|---|
| Questions | 10 |
| Suggested time | 20 |
| Difficulty mix | Foundation 3 · Intermediate 3 · Challenge 3 · Error redo 1 |
| Chapter | Chapter: DSE Physics Resistance and Circuits |
| Level | Paper 3 (challenge) |
02 Questions (10 items)
- FoundationResistors of 10, 15 and 30 ohms are joined in parallel. Find the total resistance.
- FoundationA 6 ohm and a 3 ohm resistor in parallel are joined in series with 4 ohms across 12 V. Find the total resistance and current.
- FoundationFor the same circuit, find the voltage across the parallel block and across the 4 ohm resistor.
- IntermediateTwo 4 ohm resistors in parallel are joined in series with 3 ohms across 10 V. Find the total resistance and current.
- IntermediateAt the same supply voltage, the resistance is halved. By what factor does the power change?
- IntermediateA 1 500 W air conditioner runs 4 hours a day for 30 days. Find the energy in kWh and the cost at 1.2 dollars per kWh.
- ChallengeA motor takes in 2 000 J of electrical energy and delivers 1 600 J of mechanical energy, the rest becoming heat. Find its efficiency.
- ChallengeA 1.5 m wire has a resistance of 9 ohms. It is cut down to 1.2 m. Find the resistance of the remaining piece.
- ChallengeA lamp is rated 6 V and 3 W. Find its normal current and resistance, and the actual power at 3 V.
- Error redoError clinic: a student keeps 3 W for a 6 V 3 W lamp run at 3 V. Find the actual power and the mistake.
03 Answers and one-line notes
| # | Answer | One-line note |
|---|---|---|
| 1 | 5.0 ohms: the reciprocals add to one fifth when put over a common denominator of thirty. | Put the three fractions over 30, add to 6 over 30, then invert. |
| 2 | The total is 6.0 ohms and the current 2.0 A: the parallel part is 2 ohms, plus 4 ohms. | Simplify a mixed circuit from the inside out: parallel block first, then add the series part. |
| 3 | The parallel block takes 4.0 V and the 4 ohm resistor 8.0 V, adding to the 12 V supply. | Series voltages must add to the supply voltage, which makes a useful check. |
| 4 | The total is 5.0 ohms and the current 2.0 A: 2 ohms from the parallel pair plus 3 ohms. | Equal resistors in parallel divide quickly: n equal branches give one nth of the value. |
| 5 | It doubles (2.0 times): P is V squared over R, so halving R doubles the power. | At fixed voltage power varies inversely with resistance, while at fixed current it varies directly. |
| 6 | 180.0 kWh costing 216.0 dollars: 1.5 kW times 4 hours times 30 days. | Work out the daily energy first, then multiply by the number of days. |
| 7 | 80.0 per cent: useful output over total input, times 100. | Efficiency is always below 100 per cent, so a larger figure means the fraction is upside down. |
| 8 | 7.199999999999999 ohms: the resistance scales with the remaining fraction of the length. | With material and area unchanged, resistance falls in proportion to the length kept. |
| 9 | The current is 0.5 A, the resistance 12.0 ohms, and at 3 V the power is 0.75 W. | Find the resistance from the rated values, then use P equals V squared over R at the new voltage. |
| 10 | The actual power is only 0.75 W: halving the voltage quarters the power, and 3 W is merely the rating. | A rated power holds only at the rated voltage; other voltages need a recalculation through the resistance. |
04 What to do after marking
- After marking, redo only the wrong items and write down which step went wrong (formula, unit, or misread number).
- Repeat the same item two days later; move to the next paper only when both attempts are correct.
- Parents only need the answer and note columns; there is no need to explain every item.
Every item follows simplify, find the total current, then work back, with a voltage-sum check at the end.Tutor Registration →
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