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Questions on EMF and internal resistance

Q4. A battery of e.m.f. s and internal resistance r is connected in series with a variable resistor R as shown in the diagram. A voltmeter is connected as shown.

s

(a)

(i) State what is meant by the e.m.f of a battery

The EMF is the energy provided by the battery per unit charge [OR potential difference across battery when no current flows ]

(ii) The reading V on the voltmeter is the voltage across R.
Why is V less than s?

When the current flows, work is done inside the battery
to overcome the resistance (hence V <s)

(3)

(b) In order to measure s and r, an ammeter is used in the circuit, as shown below.

s

The value of R is decreased in steps and at each step the readings V and I on the voltmeter and ammeter, respectively, are recorded. These are shown in the table.

Reading on voltmeter/V
Reading on ammeter/A
4.0
0.07
3.0
0.14
2.0
0.21
1.0
0.28

 

(i) Plot a graph of V (on y axis) against I (on x axis) and draw the best straight line through the points.

  • suitable scale for I
  • four correct points
  • best fit straight line

(ii) Determine the values ofs and r from the graph, explaining your method.

s= Ir + V so, V = – rI + s This is an equation of a straight line (Y = mx + c)
  • intercept = s = 5 V
  • gradient = –r
so, r = 14.(2)

(8)
(Total 11 marks)