Aim for FivePhysics 2

Mathematical routines (MR)

Currents and power in a three-resistor circuit

  • Unit 11
  • 10 points
  • About 22 minutes

You can use a calculator on this question, just like on exam day.

A multipart problem where you use math to analyze a physical situation. You draw or sketch a representation such as a circuit diagram, a ray diagram or a graph, derive an equation using letters, calculate a numerical answer with units, and then make a claim or prediction and justify it with physics reasoning. On the exam: Question 1 of 4. New for May 2027: the free-response section is 95 minutes, down from 100, for all 4 questions (50% of your score), one of each type in this order. Calculator and equation sheet allowed. The CED suggests 20–25 minutes. This question type started in May 2025, so Physics 2 free-response questions from 2024 and earlier are built differently.

The question

An ideal 12.0 V battery is connected to three resistors. Resistor R₁ = 4.0 Ω is connected to the battery's positive terminal. Its other end connects to junction X. From junction X, two branches lead to junction Y: one branch contains R₂ = 6.0 Ω and the other contains R₃ = 12.0 Ω. Junction Y connects to the battery's negative terminal. Let I₁, I₂ and I₃ be the currents in R₁, R₂ and R₃.

Suggested time: 22 minutes

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Part (a)

2 points

Using Kirchhoff's rules, write a junction equation and two independent loop equations that relate I₁, I₂ and I₃. Use numerical values for the battery and the resistances.

Type math plainly, like x^2, sqrt(x) or (x+1)/(x−1).

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Part (b)

3 points

Calculate I₁, I₂ and I₃.

Type math plainly, like x^2, sqrt(x) or (x+1)/(x−1).

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Part (c)

2 points

(i) Calculate the power dissipated in each resistor. (ii) Show that your results are consistent with conservation of energy.

Type math plainly, like x^2, sqrt(x) or (x+1)/(x−1).

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Part (d)

3 points

Resistor R₃ is removed, leaving a gap in its branch. (i) Does the current in R₁ increase, decrease or stay the same? (ii) Does the potential difference across R₂ increase, decrease or stay the same? Justify both claims. (iii) Calculate the new potential difference across R₂.

Type math plainly, like x^2, sqrt(x) or (x+1)/(x−1).

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