A student investigates the effective resistance of different combinations of resistors and lamps in circuits. The student sets up the circuit shown in Fig. 2.1. A power supply V [Figure 2.1]

1. (a)(i)The student: • closes the switch • measures the potential difference V₁ across the resistors and the current I₁ in the circuit • opens the switch. The readings on the voltmeter and ammeter are shown in Fig. 2.2 and Fig. 2.3. 0 1 2 V [Figure 2.2] 3 0.4 0.5 0.6 0.3 0.7 0.2 0.8 A 0.1 0.9 1 [Figure 2.3] Record the potential difference V₁ and the current I₁ shown in Fig. 2.2 and Fig. 2.3. V₁ = V I₁ = A [2][2]
2. (a)(ii)Calculate the effective resistance R₁ of the combination of resistors using the equation: R₁ = V₁ I₁ R₁ = Ω [1][1]
3. (a)(iii)Suggest why the switch is opened after the readings of potential difference and current have been taken. [1][1]
4. (b)The student: • rearranges the circuit so that the resistors are connected as shown in Fig. 2.4 • closes the switch • measures the potential difference V₂ and the current I2 • opens the switch. 2 power supply A V [Figure 2.4] The new readings are: V₂ = 2.8V I2 = 0.88A Calculate the effective resistance R₂ of the combination of resistors using the equation: R₂ = V₂ I2 Record your answer on the answer line. Write down the value of 2R2 R2 = Ω 2R2 = Ω [1][1]
5. (c)If the resistors are identical, theory suggests that R₁ = 2R2. Two quantities can be considered to be equal within the limits of experimental accuracy if their values are within 10% of each other. State whether the results indicate that the resistors are identical. Support your statement with a calculation. calculation statement [2][2]
6. (d)The student repeats the experiments in (a) and (b) but replaces the resistors with lamps. He obtains the following results: The effective resistance R3 of the combination of lamps connected as in Fig. 2.1 is 5.2Ω. The effective resistance R₄ of the combination of lamps connected as in Fig. 2.4 is 3.4Ω. The teacher explains that the resistance of the lamp filaments changes due to a heating effect and therefore R3 is not equal to 2R4. Suggest one observation that the student makes while doing the experiment that supports the teacher's explanation. [1][1]
7. (e)The student extends the investigation using a different combination of the three lamps to the two combinations already used in (a) and (b). Complete the circuit diagram in Fig. 2.5 to show a third way of connecting three lamps between X and Y. X A power supply V Y [Figure 2.5] [2][2]

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