Logarithmic and linearised graphs — WPH16 IAL Physics practice questions · Study-IAL

Subjects
Physics
WPH16
6.2

Logarithmic and linearised graphs

WPH16Topic 6.22 questions

Using log-linear and log-log graphs to test exponential and power-law relationships and determine constants.

Specification points

Plot results on a graph using an appropriate scale and units; the graph could be logarithmic in nature
Use logarithmic plots to test exponential and power law variations, e.g. plotting $\ln y$ against $x$ for $y = Ae^{kx}$ and against for

Previous topic6.1Combining uncertainties Next topic 6.3Core practicals review

Aekx

\ln y

\ln x

y = Ax^n

Comment on the trend/pattern obtained

Determine the relationship between two variables or determine a constant with the aid of the graph, e.g. by determining the gradient using a large triangle

Perform calculations, using the correct number of significant figures

Suggest realistic modifications to reduce errors and to improve the experiment

Stuck on something?

Get a plain-language explanation, a worked example and the usual mistake.

Questions

Multiple choice: 1
Calculation: 1
Total: 2

Sample questions

Original practice questions written in the style of the exam.

Question 14 marks
A capacitor discharges through a $100\,\text{k}\Omega$ resistor. The potential difference $V$ across it is given by $V = V_0e^{-t/RC}$ .

(a) Explain why a graph of $\ln V$ against $t$ is a straight line.

(b) The gradient of this graph is $-0.045\,\text{s}^{-1}$ . Calculate the capacitance.
Mark scheme
- Taking natural logs: $\ln V = \ln V_0 - \dfrac{t}{RC}$ (1)

This has the form

y = mx + c

with

y = \ln V

x = t

, gradient

-1/RC

and intercept

\ln V_0

(1)

RC = 1/0.045 = 22\,\text{s}

(1)

C = 22/(100 \times 10^{3}) = 2.2 \times 10^{-4}\,\text{F}

(

220\,\mu\text{F}

) (1)