Electrical Quantities (Cambridge (CIE) IGCSE Physics): Exam Questions

A student is investigating a power supply. She is using the circuit shown in Fig. 3.1.

The student connects the crocodile clip to a length l = 100.0 cm of the resistance wire and measures the potential difference V₀ across terminals P and Q and the current I₀ in the circuit.

(i) Record the values of V₀ in V, and I₀ in A, shown on the meters in Fig. 3.2 and Fig. 3.3.

V₀ = ........................................................... V

I₀ = ........................................................... A [1]

(ii) Calculate the resistance R₀ of 100.0 cm of the wire. Use your values of V₀ and I₀ and the equation 

R₀ = ...........................................................Ω [1]

The student then connects the crocodile clip to lengths l = 70.0 cm, 60.0 cm, 50.0 cm, 40.0 cm and 30.0 cm of the resistance wire. She measures the current I in the circuit for each length.

Her readings are shown in Table 3.1.

Table 3.1

Calculate, and write in Table 3.1, the value of for length l = 70.0 cm of the wire.

Plot a graph of  / cm (y-axis) against (x-axis). You do not need to start your axes at the origin (0,0).

(i) Determine the gradient G of the graph. Show clearly on the graph how you obtained the necessary information.

G = ........................................................ [1]

(ii) Calculate the electromotive force (e.m.f.) E of the power supply. Use your value of R₀ from (a)(ii) and the equation 

, where k = 100 cm.

E = ........................................................ [1]

The ammeter in this circuit has a small resistance which affects the current. The effect of this resistance on the measured current I will be different for each measured length l of the resistance wire.

State and explain which length l will be most affected by the resistance of the ammeter.

A student is determining the resistance of a piece of wire.

    Fig. 2.1 shows the circuit she uses.

Record the current in the circuit, as shown on the ammeter in Fig. 2.2.

= ........................................................ 

The student places the sliding contact C at a distance = 20.0 cm from P. The voltmeter reading is shown in Fig. 2.3. Record the voltmeter reading in Table 2.1 for  = 20.0 cm.

Table 2.1

The student repeats the procedure using values of = 40.0 cm, 60.0 cm, 80.0 cm and 100.0 cm. The readings are shown in Table 2.1.

Complete the column headings in the table.

Table 2.1

Plot a graph of V / V (y-axis) against / cm (x-axis). Start both axes at the origin (0, 0).

Extended tier only

(i) Determine the gradient G of the graph. Show clearly on the graph how you obtained the necessary information.

G = ........................................................ [2]

(ii) Calculate the resistance R of each centimetre of the wire. Use the following equation:

,

where k = 1.0 V/cm and where  is the current recorded in (a).

  Include the unit.

R = ........................................................ [2]

A student is investigating a resistance wire. She uses the circuit shown in Fig. 3.1.

(i) On Fig. 3.1, draw a voltmeter connected to measure the potential difference V across terminals P and Q.

[1]

(ii) The student connects the crocodile clip to a length  = 90.0 cm of the resistance wire and measures the potential difference V across terminals P and Q and the current  in the circuit.

Read, and record in Table 3.1, the values of V and  shown on the meters in Fig. 3.2 and Fig. 3.3.

[2]

Table 3.1

The student then connects the crocodile clip to lengths  = 60.0 cm and  = 40.0 cm of the resistance wire. She measures the potential difference V across terminals P and Q and the current  in the circuit. Her readings are shown in Table 3.1.

Complete the column headings in Table 3.1.

(i) Calculate, and record in Table 3.1, the resistance R of each length  of the wire.

Use the readings from Table 3.1 and the equation 

[2]

(ii) Calculate, and record in Table 3.1, the value of R/ for each length of wire.

[1]

Use your results in Table 3.1 to calculate the resistance R₂₅ of a 25.0 cm length of the resistance wire. Show your working.

R₂₅ = ..................................................... Ω 

Suggest one reason why different students, carrying out the experiment carefully with the same equipment, may not obtain identical results.

The student finds that, during the experiment, the wire becomes hot because of a high current.

She decides to use a variable resistor to prevent this.

Complete the circuit in Fig. 3.4 to show a variable resistor used for this purpose in the experiment.

A student is determining the resistance of a resistance wire.

The circuit is shown in Fig. 2.1.

Record, in amperes A, the current  in the circuit, as shown on the ammeter in Fig. 2.2.

= ........................................................ 

The student places the sliding contact C at a distance  = 20.0 cm from B.

  She records the potential difference V across the length  of the resistance wire.

  She repeats the procedure using  values of 40.0 cm, 60.0 cm, 80.0 cm and 100.0 cm. All the readings are shown in Table 2.1.

Calculate, and record in Table 2.1,  for each value of .

Complete the  column heading.

Table 2.1

Look carefully at the values in Table 2.1.

(i) Tick the box to show your conclusion from the results.

  is approximately constant.

  is decreasing as V increases.

  is increasing as V increases.

There is no simple pattern for in the results.

[1]

(ii) Justify your conclusion by reference to your results.

[1]

Calculate the resistance of 100 cm of the resistance wire.

Use the equation where V is the potential difference across 100 cm of the resistance wire. Use the value of current  from part (a). Give your answer to a suitable number of significant figures for this experiment and include the unit.

R = ........................................................ 

In this type of experiment, it is sensible to keep the temperature of the resistance wire as close to room temperature as possible. Suggest one way to minimise the rise in temperature of the resistance wire.

Draw the circuit symbol for a variable resistor.

A student is investigating the relationship between the power produced by an electrical heater and the time taken to heat a beaker of water. The power of the heater is given by the equation P = VI, where V is the potential difference (p.d.) across the heater and I is the current in the heater.

    Plan an experiment to investigate the relationship between the power produced by an electrical heater and the time taken to heat a beaker of water.

    The following apparatus is available:  

ammeter voltmeter 0–12 V variable power supply

250 cm³ beaker heater thermometer stopwatch

The student can also use other apparatus and materials that are usually available in a school laboratory.  

You should:

• complete the diagram in Fig. 4.1 to show the circuit that you would use

• explain briefly how you would carry out the investigation

• state the key variables that you would control

• draw a table with column headings, to show how you would display your readings (you are not required to enter any readings in the table)

• explain how you would use your results to reach a conclusion.

A student investigates the resistance of a wire. 

Fig. 3.1 shows the circuit he uses.

The student measures the current and decides that he wants to use a lower current. 

He adds a variable resistor to the circuit to reduce the current. 

On Fig. 3.1, mark with an X a suitable position in the circuit for the variable resistor.

The student measures the current I in the circuit. Record the current shown in Fig. 3.2. 

I = ........................................................

The student places the sliding contact at a distance = 85.0cm from B. 

He measures, and records in Table 3.1, the potential difference (p.d.) V across the length of resistance wire BC. 

Record, in Table 3.1, the potential difference shown in Fig. 3.3.

The student repeats the procedure using values of 65.0 cm, 45.0 cm, 25.0 cm and 5.0cm. His readings are shown in Table 3.1. 

(i) Calculate, and record in Table 3.1, the resistance R of 85.0 cm of the resistance wire using the equation

[1]

(ii) Complete the column headings in Table 3.1.

Table 3.1

[1]

Plot a graph of resistance R (y‑axis) against length l (x‑axis). Start both axes at the origin (0,0).

Use your graph to determine the resistance R₅₀ of 50.0cm of the resistance wire. 

Show clearly on the graph how you obtained the necessary information. 

R₅₀ = ...........................................................

 A student is investigating a resistance wire. She uses the circuit shown in Fig. 2.1.

(i) On Fig. 2.1, draw a voltmeter connected to measure the potential difference (p.d.) V across terminals P and Q. 

[1]

(ii) The student connects the crocodile clip to a length l = 90.0 cm of the resistance wire and measures the potential difference V across terminals P and Q and the current I in the circuit.

Read, and record in Table 2.1, the values of V and I shown on the meters in Fig. 2.2 and Fig. 2.3.

                                                                                                                           [2]

The student then connects the crocodile clip to lengths l = 60.0 cm and l = 40.0 cm of the resistance wire. She measures the potential difference V across terminals P and Q and the current I in the circuit. Her readings are shown in Table 2.1. 

Complete the column headings in Table 2.1.

Table 2.1

(i) Calculate, and record in Table 2.1, the resistance R of each length l of the wire. 

Use the readings from the table and the equation  

[2]

(ii) Calculate, and record in Table 2.1, the value of for each length l of the wire. 

[1]

Another student suggests that the values of for each length of wire should be the same. 

State whether the results support this suggestion.

Justify your statement with reference to values from the results. 

Suggest one difficulty which explains why different students, doing the experiment carefully with the same equipment, may not obtain identical results.

A student finds that during the experiment, the wire becomes hot because there is a high current. 

He decides to use a variable resistor to prevent this. 

(i) Draw an X on the circuit in Fig. 2.1 to show where a variable resistor is connected for this purpose in the experiment.

 [1]

(ii) In the space below, sketch the circuit symbol for a variable resistor. 

[1]