Sunday, March 1, 2015

Physics 9702 Doubts | Help Page 73

  • Physics 9702 Doubts | Help Page 73

Question 392: [Current of Electricity]
The diagram shows a metal filament lamp connected in series with an ammeter, battery and a variable resistor. A high resistance voltmeter is connected across the lamp.

Which graph represents the variation of I, the current through the lamp, with the potential difference V across it?

Reference: Past Exam Paper – N93 / I / 12

Solution 392:
Answer: A.
As the p.d. V across the metal filament lamp increases, the temperature of the metal filament increases. This causes it resistance to increase. So, it does not always follow Ohm’s law. [C is incorrect]

Also, since the resistance increases, the current would tend to decrease at higher values of V. [D and E are incorrect] Graph B would be correct if only the lamp was connected in the circuit (given the e.m.f is not too big), without the variable resistor. [B is incorrect]

Let the resistance of the lamp be R­L and the resistance of the variable resistor be Rr. Let the e.m.f. of the supply be E. From the potential divider equation, the p.d. V across the lamp is given by
V = [RL / (RL+Rr)] E
If the p.d. V across the lamp is increasing, it means the Rr is decreasing since E is constant.

The current I through the lamp is the current in the whole circuit since this is a series connection. The current I is given by I = E / (RL+Rr).

Since Rr is decreasing, at some point when Rr = 0, the current would tend to I = E / RL where E would be equal to V. RL would be given by RL = V / I. Since RL is increasing and E (= V) is constant, the current I would be smaller at higher values of V. So, the gradient of the graph should decrease at higher values of V.

Question 393: [Waves > Stationary waves]

Diagram shows a standing wave on a string. The standing wave has three nodes N1, N2 and N3.

Which statement is correct?
A All points on the string vibrate in phase.
B All points on the string vibrate with the same amplitude.
C Points equidistant from N2 vibrate with the same frequency and in phase.
D Points equidistant from N2 vibrate with the same frequency and the same amplitude.

Reference: Past Exam Paper – November 2009 Paper 11 Q25 & Paper 12 Q24 & June 2013 Paper 13 Q28

Solution 393:
Answer: D.
A and B are obviously wrong. The points on the string (forming a stationary wave) do not vibrate in phase not with the same amplitude.

Points within a loop (example: N1-N2 loop or N2-N3 loop) vibrate in phase, but the points in a loop vibrate out of phase with the points in the adjacent loop. For example, if the points in the loop N1-N2 move upwards, then the points in the loop N2-N3 will move downwards. Remember that even if a node is shown as an oval (with an upper and lower arc), only one of these arc is present at a particular time. If the upper arc of the loop N1-N2 is present, then the lower arc of the loop N2-N3 will be present. [A is incorrect]

All the points on the string do not vibrate with the same amplitude (amplitude is the maximum displacement from the equilibrium position). Points closer to the nodes have a smaller amplitude and antinodes are points with maximum amplitude. [B is incorrect]

The points equidistant from node N2 vibrate with the same frequency and the same amplitude, but not in phase since points in adjacent loops are out of phase. If one such point in loop N1-N2 is moving downwards, then the corresponding point equidistant from node N2 in loop N2-N3 would be moving upwards. [C is incorrect]

Question 394: [Waves > Stationary waves]
Diagram shows steel wire clamped at one end and tensioned at the other by a weight hung over a pulley.

Vibration generator is attached to wire near the clamped end. Stationary wave with one loop is produced. Frequency of the vibration generator is f.
Which frequency should be used to produce stationary wave with two loops?
A f / 4                          B f / 2                          C 2f                             D 4f

Reference: Past Exam Paper – June 2010 Paper 11 Q25 & Paper 12 Q22 & Paper 13 Q24

Solution 394:

Answer: C.
Let the length of wire = L

In the case shown (1 loop is formed – this is called the 1st harmonic), half a wave is formed (with 2 nodes). So, L = λ1 / 2 where λ is the wavelength of the wave formed.

Wavelength λ1 = 2L

Speed v = f λ
Therefore, the frequency of the vibration generator for which the wave shown is produced, f1 = v / λ1 = v / 2L. (this is given as f in the question: f1 = f)

The length of wire used is the same (= L).

For 2 loops to be produced (this is called the 2nd harmonic), the length of wire L = λ2 since a complete wave would then be formed with 3 nodes, where is λ2 is the wavelength of the new wave formed.
So, the new frequency f2 = v / λ2 = v / L = 2f1 = 2f

Question 395: [Capacitors]
A 2.0 μF capacitor is charged to a potential difference (p.d.) of 50 V and a 3.0 μF capacitor is charged to a p.d. of 100 V.
Calculate the charge on the plates of each capacitor and the energy stored by each.              [4]

The capacitors are then joined together in parallel with their positive plates connected together.

What is the equivalent capacitance of this combination?       [1]
Hence calculate the total energy stored by the capacitors after connection.  [3]
Suggest why there is a loss of stored energy when the capacitors are connected.     [2]

Reference: Past Exam Paper – Edexcel January 2003 PHY5 Q1

Solution 395:
Charge of capacitor, Q = CV
For 1st capacitor, Q1 = CV = (2.0x10-6) (50) = 1.0x10-4C
For 2nd capacitor, Q2 = CV = (3.0x10-6) (100) = 3.0x10-4C

Energy stored in capacitor, W = ½ CV2  
Energy stored in 1st capacitor, W1 = ½ CV2 = 0.5 (2.0x10-6) (50)2 = 2.5x10-3J
Energy stored in 2nd capacitor, W2 = ½ CV2 = 0.5 (3.0x10-6) (100)2 = 1.5x10-2J

The capacitors are now joined together in parallel with their positive plates connected together.

For a parallel combination of capacitors,
Equivalent capacitance, Ctotal = C1 + C2 = 2.0 + 3.0 = 5.0 μF

After connection,
Total Charge = (1.0x10-4) + (3.0x10-4) = 4.0x10-4 C

Total energy stored, Etotal = ½ (Q2 / C) = 0.5 [(4.0x10-4)2 / (5.0x10-6)] = 0.016 J

There’s loss of stored energy when the capacitors are connected
EITHER due to gain in internal energy during electrical work
OR because of the heating in the wires resulting in the dissipation of thermal heat
OR due to work done in charges
OR because energy is needed to overcome resistance in wires

Question 396: [Kinematics]
A student, standing on the platform at a railway station, notices that the first two carriages of an arriving train pass her in 2.0s, and the next two in 2.4s. The train is decelerating uniformly. Each carriage is 20m long. When the train stops, the student is opposite the last carriage. How many carriages are there in the train?

Reference: “Cambridge International As and A level Physics,” 2nd edition, by Mike Crundell, Geoff Goodwin and Chris Mee, Chapter 3 (Kinematics) Q2

Solution 396:
1 carriage is 20m long.

Equation for uniformly accelerated motion: s = ut + ½ at2
Let the initial speed with which the train starts to pass her = u
The deceleration is uniform.

For 1st 2 carriages: Total distance = 2 (20) = 40m and time taken = 2.0s
40 = u(2) + ½ (a)(2)2
40 = 2u + 2a
20 = u + a                                …………….. (1)

For 2nd 2 carriages: We don’t know with what speed the 2nd 2 carriages start to pass her. So, now we consider the motion of the 1st 4 carriages of the train. Total distance = 4 (20) = 80m and total time taken = 2.0 + 2.4 = 4.4s
80 = u(4.4) + ½ (a)(4.4)2
80 = 4.4u + 9.68a                    …………….. (2)

From eq(1),
u = 20 – a                                …………….. (3)

Replace u = 20 – a in eq(2)
80 = 4.4(20 – a) + 9.68a
-8 = 5.28a
Acceleration, a = - 1.52 ms-2

From eq(3),
Initial speed, u = 20 – (-1.52) = 21.52 ms-1

Now, let the total length of the carriages = s. Initial speed, u = 21.52ms-1. Final speed = 0ms-1 (the train stops). Acceleration, a = - 1.52ms-1.
v2 = u2 + 2as
0 = (21.52)2 + 2 (-1.52) s
Total length, s = 152.34m

Number of carriages = 152.34 / 20 = 7.62 = 8
{The number of carriages can only be an integer. Since the student is opposite the last train, the number of carriages = 8.}

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