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Mathematical Requirements (Appendix C)

Linearising a relationship to find a constant

  • 3 things to know
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Overview

Recall questions on Linearising a relationship to find a constant.

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Key term

For capacitor discharge, what transformation must be applied to voltage readings before plotting to obtain a straight line?

Key term

What does the gradient of a ln V against time graph represent for capacitor discharge?

Numbers

How do you calculate the time constant τ from the gradient of a ln V against time graph?

Questions from this subtopic

Each one with the model answer underneath.

  1. 1

    On a displacement–time graph, how is mean velocity represented graphically?

    Model answer

    By the gradient of a chord drawn between two points on the curve.

  2. 2

    How can the value of g be extracted from a distance–time graph of a falling object?

    Model answer

    By analysing the curvature, or by using gradient analysis or curve fitting methods based on s = ½gt².

  3. 3

    For capacitor discharge, what transformation must be applied to voltage readings before plotting to obtain a straight line?

    Model answer

    Take the natural logarithm of the voltage readings.

  4. 4

    What does the gradient of a ln V against time graph represent for capacitor discharge?

    Model answer

    The negative reciprocal of the time constant (−1/τ).

  5. 5

    How do you calculate the time constant τ from the gradient of a ln V against time graph?

    Model answer

    τ equals the negative reciprocal of the gradient: τ = −1/gradient.

  6. 6

    Calculate the time constant when gradient = -0.17 s⁻¹.

    Model answer

    Time constant = −1 ÷ gradient = −1 ÷ (−0.17 s⁻¹) = 5.9 s.

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