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Electric Circuits

Combining resistances in series and parallel

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Overview

Recall questions on the series and parallel equations, why a parallel combination is smaller than its smallest member, and what adding another branch does.

What you need to know

Answer each one before you reveal it.

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Numbers

How is the total resistance of a parallel combination found, and how does the total current relate to the branch currents?

Questions from this subtopic

Each one with the model answer underneath.

  1. 1

    How is the equation for resistors in series derived from energy conservation?

    Model answer

    Energy conservation gives V = V₁ + V₂ + V₃, and the current I is the same in each, so IR = IR₁ + IR₂ + IR₃, giving R = R₁ + R₂ + R₃.

  2. 2

    How is the equation for resistors in parallel derived from charge conservation?

    Model answer

    Charge conservation gives I = I₁ + I₂ + I₃, and the potential difference V is the same across each, so V/R = V/R₁ + V/R₂ + V/R₃, giving 1/R = 1/R₁ + 1/R₂ + 1/R₃.

  3. 3

    State the equation for the total resistance of resistors connected in parallel:

    Model answer

    1/R = 1/R₁ + 1/R₂ + 1/R₃, where R is the total resistance.

  4. 4

    A 4.0 Ω resistor and a 6.0 Ω resistor are connected in parallel. What is their combined resistance?

    Model answer

    1/R = 1/4.0 + 1/6.0 = 5/12, so R = 2.4 Ω.

  5. 5

    Why is the resistance of a parallel combination always smaller than the smallest single resistance in it?

    Model answer

    Adding another branch gives the charge an extra path, increasing the total current for the same potential difference and so reducing the overall resistance.

  6. 6

    Two identical resistors of resistance R are connected in parallel. What is their combined resistance?

    Model answer

    The combined resistance is R/2.

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