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 \(\frac{1}{e}\).

State the value of the intercept on the *R* axis.

**Answer/Explanation**

## 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*

«–» *r*

*Allow answer in words*

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.

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.

State what is meant by a zero error.

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).

**Answer/Explanation**

## Markscheme

a.

correct labelling of both instruments

**[1 mark]**

*V = E – Ir*

large triangle to find gradient and correct read-offs from the line**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]*

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]*

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]*