A student investigates series and parallel combinations of resistors. The student is provided with two resistors, X and Y, connected in the circuit shown in Fig. 2.1. The resistors are not identical. The electromotive force (e.m.f.) of the power supply is 3.0V. [Figure 2.1]

1. (a)(i)• The student closes the switch. Fig. 2.2 shows the readings Vₓ on the voltmeter and Iₛ on the ammeter. Record the readings of Vₓ and Iₛ. [Figure 2.2] Vₓ = .................................................... V Iₛ = .................................................... A[2]
2. (a)(ii)The resistance of a resistor can be found using the equation: resistance = voltage across the resistor / current in the resistor Calculate Rₓ, the resistance of resistor X. Rₓ = .................................................... Ω[1]
3. (a)(iii)Suggest why the switch is opened after the readings of potential difference and current are recorded.[1]
4. (a)(iv)• The student disconnects the voltmeter and reconnects it across resistor Y. The potential difference Vᵧ across Y is given by the equation: Vᵧ = 3.0 - Vₓ Using this equation and your value of Vₓ from (a)(i), calculate Vᵧ. Calculate the resistance Rᵧ of Y. Vᵧ = .................................................... V Rᵧ = .................................................... Ω[1]
5. (b)(i)• The student now connects X and Y in parallel. Complete the circuit diagram in Fig. 2.3 to show the two resistors connected in parallel between points W and Z. Draw the voltmeter connected to measure the potential difference Vₚ across both resistors. [Figure 2.3][2]
6. (b)(ii)Theory suggests that, if the two resistors are arranged in parallel, the combined resistance Rₜ is given by: Rₜ = (RₓRᵧ) / (Rₓ + Rᵧ) Use the equation and your values of Rₓ and Rᵧ from (a)(ii) and (a)(iv) to calculate Rₜ. Rₜ = .................................................... Ω[1]
7. (b)(iii)The manufacturer suggests that the combined resistance of resistors X and Y when placed in parallel is 2.5Ω. 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 your value of Rₜ calculated in (b)(ii) has the same value as that suggested by the manufacturer. Support your statement with a calculation. calculation statement[2]

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