CAPE Physics Unit 2 · 2013 · Paper 2

40 questions and parts from this paper. Open one to see it in full, then practise it on Quelpr and get it marked against the mark scheme.

1. 1(a)6 marksWith the aid of a diagram, derive the formula for the equivalent resistance of two resistors in parallel.
2. 1(b)(i)2 marksCalculate the equivalent resistance, R_eq, in Figure 1B.
3. 1(b)(ii)1 markDetermine the voltage, V2.
4. 1(c)(i)3 marksUse the results in Table 1 to plot a graph of I against V_T on the grid provided.
5. 1(c)(ii)3 marksThe slope, S, of the graph is related to the internal resistance, r, by S = -1/r Ω^-1. Find S and hence determine the internal resistance, r, of the battery.
6. 2(a)(i)1 markUse the graph to determine the open loop d.c. gain of the amplifier.
7. 2(a)(ii)1 markUse the graph to determine the unity gain bandwidth of the amplifier.
8. 2(a)(iii)1 markUse the graph to determine the open loop bandwidth of the amplifier.
9. 2(b)(i)3 marksDraw the circuit diagram for this amplifier and label the resistors with their values.
10. 2(b)(ii)2 marksCalculate the gain of the amplifier.
11. 2(b)(iii)2 marksUse the open loop gain-frequency curve in Figure 2 to determine the closed loop bandwidth of this amplifier.
12. 2(b)(iv)2 marksDeduce the gain of the amplifier when the input resistance is made infinitely large (effectively removed from the circuit).
13. 2(b)(v)1 markWhat would be the input impedance of the resulting circuit?
14. 2(b)(vi)2 marksIdentify the practical application for the circuit and state why it is suited for this application.
15. 3(a)3 marksDescribe the phenomenon of 'photoelectric emission'.
16. 3(b)2 marksIdentify the property of a light source that would make it suitable for a demonstration of this phenomenon and give a reason why this property makes it suitable.
17. 3(c)3 marksCalculate the energy (in eV) of a light photon of wavelength 200 nm.
18. 3(d)3 marksCalculate the maximum velocity of the electrons ejected from the surface.
19. 3(e)(i)3 marksOn the grid provided, plot a graph of V_s against λ. Ensure that the λ scale extends to 550 nm.
20. 3(e)(ii)1 markFrom the graph determine the cut-off wavelength for Caesium.
21. 4(a)(i)2 marksBy equating the gain in kinetic energy of the electrons to the work done in accelerating them, show that the velocity, v_e, of the emerging beam electrons is given by v_e = sqrt((2 e V_p) / m_e).
22. 4(a)(ii)2 marksCalculate the velocity of the electrons in the emerging electron beam when V_p = 25 kV.
23. 4(b)(i)3 marksCalculate the magnitude and direction of the magnetic field inside the solenoid.
24. 4(b)(ii)a)2 marksExplain the effect on the electron's horizontal velocity component, resulting from its interaction with the B-field.
25. 4(b)(ii)b)2 marksDescribe the effect on the electron's vertical velocity component.
26. 4(b)(ii)c)4 marksDescribe the resultant motion of the electrons and the nature of the image produced on the phosphorescent screen when the B-field is large enough to prevent the electrons from touching the interior of the solenoid.
27. 5(a)3 marksUse logic Y to represent the output of this system and draw up the truth table for the operation of the headlight automatic switching circuit. Write the logic equation represented by this truth table.
28. 5(b)(i)3 marksIn this circuit, the open loop operational amplifier is used to compare the surrounding lighting level with a preset value. Explain how this is done.
29. 5(b)(ii)2 marksJustify the need for the light dependent resistor (LDR) in the circuit.
30. 5(b)(iii)2 marksDescribe how a relay functions, stating why this device is necessary in the circuit.
31. 5(c)(i)3 marksReplace the circuit in the dashed box, P, with one consisting of NAND gates only.
32. 5(c)(ii)2 marksThe 7400 chip has 4 NAND gates. How many 7400 chips are required for the NAND-equivalent circuit drawn in Part c (i)?
33. 6(a)1 markWrite the equation describing this decay.
34. 6(b)(i)1 markWrite the equation expressing τ in terms of R and C.
35. 6(b)(ii)1 markIf the capacitive discharge is used to model radioactive decay, where voltage is the analogue of number of particles, what would be the relationship between time constant, τ, and decay constant, λ?
36. 6(b)(iii)3 marksGiven that t_1/2 is the half-life of a radioactive sample, use the decay equation from Part (a) to show that t_1/2 = 0.69 / λ.
37. 6(c)(i)2 marksDescribe the change in the voltages across R and C, both of which initially had no voltage across them.
38. 6(c)(ii)4 marksAfter a sufficiently long time, voltages across R and C become stable and S1 is switched to terminal b to model decay. Using R = 1 MΩ, calculate the value of C needed to model the radioactive decay of Francium-221.
39. 6(d)(i)1 markState what is meant by the term 'activity' of a radioactive nucleus and write its expression in mathematical form.
40. 6(d)(ii)2 marksA sample of Francium-221 contains 10^12 atoms. Calculate its activity.