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Section III · Topic guide

Electricity & circuits

Section III — Sciences · a free, hand-written guide with worked reasoning and adaptive practice that finds your weak spots.

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The short answer

Voltage, current and resistance tied together by Ohm's law — and how series and parallel circuits differ.

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Free interactive lesson

Try the reasoning style

Section I · Humanities & Social SciencesSample question

We treat forgetting as a failure — a lapse to be patched with reminders and records. Yet a mind that kept everything could not think; it would drown in the undifferentiated noise of every moment it had ever lived. To forget is not so much to lose information as to decide, mostly without our noticing, what was never worth keeping.

The author's argument relies most directly on which unstated assumption?

Pick an option to see how the tutor reasons to the answer — not just whether you were right.

How to reason to the answer

Not quite — the answer is B.

Work backwards from the conclusion: a mind that ‘kept everything’ supposedly ‘could not think.’ That only follows if thinking means leaving most of experience out — so B is the premise the argument quietly rests on. A raises reliability, which the passage never weighs; C contradicts ‘mostly without our noticing’; D smuggles in a claim about intellect the passage never makes. The question rewards finding the hidden premise, not recalling a fact.

A circuit is plumbing for charge: voltage () pushes, resistance () restricts, and current () flows. One equation links them — Ohm's law, — and most circuit questions are just that plus knowing how series and parallel circuits behave.

The Organic Chemistry Tutor — current, voltage, resistance and power, with problems.

The two equations

Ohm's law: (voltage = current × resistance). Power: . Rearrange Ohm's law as needed: and .

Series vs parallel

Series (one loop)

  • Same CURRENT through every component
  • Voltages ADD up
  • Resistances ADD:
  • One break stops the whole circuit

Parallel (branches)

  • Same VOLTAGE across each branch
  • Currents ADD up
  • Total resistance is LESS than the smallest branch

The parallel-resistance trap

Adding resistors in parallel lowers the total resistance — it's always less than the smallest individual resistor, because you've given the current more paths to flow through. Many students wrongly expect resistance to go up.

Worked example

A 12 V battery drives two resistors, 4 Ω and 2 Ω, connected in series. What is the current in the circuit?

Check yourself

Two identical resistors are connected in parallel. Compared with one resistor alone, the total resistance is:

The paper prints one set of measurements and asks several questions on it, and the numbers rarely come out as clean as a textbook's — a real battery is not an ideal source. Below is that shape.

Passage· 3 questions on it

The following is adapted from a school physics practical.

A battery marked 12.0 V was connected to identical lamps, each of resistance 6.0 Ω. In each arrangement the current drawn from the battery and the voltage across the battery's terminals were measured.
ArrangementLampsTotal resistance of the lamps (Ω)Current from battery (A)Terminal voltage (V)
Ione lamp6.01.8511.1
IItwo in series12.00.9611.5
IIItwo in parallel3.03.4310.3
IVthree in parallel2.04.809.6
The terminal voltage is the voltage actually delivered to the lamps. It is lower than the 12.0 V marked on the battery because the battery has some resistance of its own, and the current has to pass through that as well.

Q1 of 3 on this passage

Arrangement IV puts three 6.0 Ω lamps in parallel and the table gives their combined resistance as 2.0 Ω. Which statement explains that figure correctly?

Q2 of 3 on this passage

What is the resistance of the battery itself?

Q3 of 3 on this passage

Which arrangement delivers the most power to the lamps, and roughly how much?

Key takeaways

  • Ohm's law: . Power: .
  • Series: same current; voltages and resistances add.
  • Parallel: same voltage; currents add; .
  • Parallel resistance is always LESS than the smallest resistor.
  • Find the total resistance first, then use Ohm's law for current.

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