# IB DP Physics Topic 5: Electricity and magnetisms Question Bank SL Paper 3

Question

An electrical circuit is used during an experiment to measure the current I in a variable resistor of resistance R. The emf of the cell is e and the cell has an internal resistance r.

A graph shows the variation of $$\frac{1}{I}$$ with R.

a.

Show that the gradient of the graph is equal to $$\frac{1}{e}$$.

[2]
b.

State the value of the intercept on the R axis.

[1]

## Markscheme

a.

«ε = IR + Ir»

$$\frac{1}{I} = \frac{R}{\varepsilon } + \frac{r}{\varepsilon }$$

identifies equation with y = mx + c

«hence m = $$\frac{1}{\varepsilon }$$»

No mark for stating data booklet equation

Do not accept working where r is ignored or ε = IR is used

OWTTE

b.

«–» r

Question

The circuit shown may be used to measure the internal resistance of a cell.

The ammeter used in the experiment in (b) is an analogue meter. The student takes measurements without checking for a “zero error” on the ammeter.

a.

An ammeter and a voltmeter are connected in the circuit. Label the ammeter with the letter A and the voltmeter with the letter V.

[1]
b.

In one experiment a student obtains the following graph showing the variation with current I of the potential difference V across the cell.

Using the graph, determine the best estimate of the internal resistance of the cell.

[3]
c.i.

State what is meant by a zero error.

[1]
c.ii.

After taking measurements the student observes that the ammeter has a positive zero error. Explain what effect, if any, this zero error will have on the calculated value of the internal resistance in (b).

[2]

## Markscheme

a.

correct labelling of both instruments

[1 mark]

b.

V = E – Ir

OR
use of intercept E = 1.5 V and another correct data point

internal resistance = 0.60 Ω

For MP1 – do not award if only $$R = \frac{V}{I}$$ is used.

For MP2 points at least 1A apart must be used.

For MP3 accept final answers in the range of 0.55 Ω to 0.65 Ω.

[3 marks]

c.i.

a non-zero reading when a zero reading is expected/no current is flowing
OR
a calibration error

OWTTE
Do not accept just “systematic error”.

[1 mark]

c.ii.

the error causes «all» measurements to be high/different/incorrect

effect on calculations/gradient will cancel out
OR
effect is that value for r is unchanged

Award [1 max] for statement of “no effect” without valid argument.

OWTTE

[2 marks]