2025 OCR AS Level Physics B (Advancing Physics) - H157 Practice Paper with Answers

A 12 V supply of negligible internal resistance is connected across a fixed resistor of resistance \(6.0\ \text{k}\Omega\) in series with a second resistor of resistance \(2.0\ \text{k}\Omega\). The output is taken across the \(2.0\ \text{k}\Omega\) resistor. What is the output potential difference?

A uniform metal wire has length \(2.0\ \text{m}\), diameter \(0.50\ \text{mm}\) and resistivity \(4.9\times10^{-7}\ \Omega\,\text{m}\). What is its resistance?

A dynamics trolley of mass \(0.80\ \text{kg}\) moves at \(1.5\ \text{m s}^{-1}\) and collides with a stationary trolley of mass \(0.40\ \text{kg}\). The trolleys stick together. What is their common speed immediately after the collision?

A resistance is found from \(R = V/I\). The potential difference is \(V = 6.0 \pm 0.1\ \text{V}\) and the current is \(I = 0.50 \pm 0.02\ \text{A}\). What is the best estimate of the absolute uncertainty in \(R\)?

An audio signal has a maximum frequency of \(5.0\ \text{kHz}\). It is digitised at the minimum sampling rate that allows it to be reconstructed, using 12 bits per sample. What is the transmission rate?

A cell of e.m.f. \(1.5\ \text{V}\) and internal resistance \(0.50\ \Omega\) is connected across a \(2.5\ \Omega\) resistor. What is the power dissipated in the internal resistance of the cell?

A thin converging lens has focal length \(10\ \text{cm}\). A small object is placed \(30\ \text{cm}\) from the lens. Which row gives the image distance and the magnitude of the linear magnification?

An LED emits photons of wavelength \(620\ \text{nm}\). What is the energy of one photon?

A copper wire has a resistance of \(2.5\ \Omega\). A second wire is made of the same copper. It is twice as long and has half the diameter of the first wire. What is the resistance of the second wire?

A potential divider is made from a \(12\ \text{V}\) supply of negligible internal resistance, a fixed resistor of \(4.0\ \text{k}\Omega\) and a light-dependent resistor (LDR) connected in series. The LDR is the lower component and has a resistance of \(2.0\ \text{k}\Omega\) in bright light. A voltmeter of very high resistance is connected across the LDR. What is the voltmeter reading in bright light?

A cell of e.m.f. \(6.0\ \text{V}\) and internal resistance \(0.80\ \Omega\) is connected across a resistor of resistance \(2.2\ \Omega\). What is the power dissipated in the internal resistance of the cell?

A trolley of mass \(0.80\ \text{kg}\) moves at \(1.5\ \text{m s}^{-1}\) along a level track and collides with a stationary trolley of mass \(0.40\ \text{kg}\). The trolleys stick together. Frictional forces are negligible. What is the speed of the trolleys immediately after the collision?

The density of a metal cube is found from its mass and the length of one side. The side is \((2.00 \pm 0.02)\ \text{cm}\) and the mass is \((21.6 \pm 0.2)\ \text{g}\). What is the percentage uncertainty in the calculated density?

An audio signal with a maximum frequency of \(5.0\ \text{kHz}\) is sampled at \(12\ \text{kHz}\) using 8 bits per sample. How much data is produced in \(30\ \text{s}\)?

A thin converging lens has a focal length of \(10\ \text{cm}\). A small object is placed \(30\ \text{cm}\) from the lens. At what distance from the lens is the real image formed?

An LED emits light of wavelength \(590\ \text{nm}\). What is the energy of one photon of this light?

A potential divider is made from a 12 V supply of negligible internal resistance, a fixed resistor of resistance \(4.7\ \text{k}\Omega\) and a thermistor connected in series. The output is taken across the thermistor and is \(3.0\ \text{V}\). What is the resistance of the thermistor?

A trolley of mass \(0.80\ \text{kg}\) moves at \(1.5\ \text{m s}^{-1}\) along a level track and collides with a stationary trolley of mass \(0.40\ \text{kg}\). The trolleys stick together. How much kinetic energy is transferred to other forms in the collision?

A ball leaves the edge of a horizontal table-top platform moving horizontally at \(8.0\ \text{m s}^{-1}\). The platform is \(4.9\ \text{m}\) above level ground. Air resistance is negligible and \(g = 9.81\ \text{m s}^{-2}\). What is the horizontal distance travelled by the ball before it hits the ground?

The resistivity of a wire is found using \(\rho = \dfrac{\pi d^2 R}{4L}\). The measurements are: diameter \(d = 0.50 \pm 0.01\ \text{mm}\), length \(L = 80.0 \pm 0.2\ \text{cm}\) and resistance \(R = 2.0 \pm 0.1\ \Omega\). What is the percentage uncertainty in the calculated resistivity?

A greenhouse sensor circuit has a 9.0 V supply connected across two fixed resistors in series. The upper resistor has resistance 4.7 kΩ and the lower resistor has resistance 2.2 kΩ. The output is taken across the lower resistor.

Calculate the output potential difference. [2]

Answer = ..... V

On a level air track, a glider of mass 0.80 kg moves at 1.5 m s\(^{-1}\) and collides with a stationary glider of mass 1.2 kg. The two gliders stick together after the collision.

Calculate the speed of the joined gliders immediately after the collision. [2]

Answer = ..... m s\(^{-1}\)

A thin converging lens of focal length 10 cm forms a real image of a small lamp placed 30 cm from the lens.

Calculate the distance from the lens to the image. [2]

Answer = ..... cm

A voice signal contains frequencies up to 4.0 kHz. It is digitised by sampling 10 000 times per second, using 12 bits for each sample.

(a) State whether this sampling rate is suitable for the signal, giving a reason. [1]

(b) Calculate the number of bits transmitted in one second. [1]

Answer = ..... bit s\(^{-1}\)

A cell of e.m.f. 1.5 V and internal resistance 0.40 Ω is connected to a resistor of resistance 2.6 Ω.

Calculate the power dissipated in the internal resistance of the cell. [2]

Answer = ..... W

A weather buoy digitises the signal from a wave-height sensor. The highest frequency component of the signal is 4.5 kHz. Each sample is stored as a 10-bit number.

(a) State the minimum sampling rate needed to reproduce the signal without loss of information. [0.5]

(b) The buoy samples at 10 kHz. Calculate the transmission rate in bits per second. [1]

(c) Calculate the number of kilobytes of data produced in 30 s at this rate. (1 byte = 8 bits, 1 kB = 1000 bytes) [1]

A thin converging lens has focal length 6.0 cm. An object 2.0 cm tall stands upright on the principal axis, 9.0 cm from the lens.

(a) On a grid with the lens at the centre, scale 1 cm : 1 cm, draw a ray diagram with two construction rays to locate the image. Mark both principal foci (F) and label the image. [1.5]

(b) Calculate the image distance and the height of the image, and state whether the image is real or virtual. Use your answers to say what your diagram should show. [1]

A technician tests three samples in a tensile rig: a copper wire, a glass rod and a polythene strip.

(a) Classify each sample as a metal, a ceramic or a polymer. [1.5]

(b) The glass rod fractures with almost no plastic deformation, whereas the copper wire stretches a long way before breaking. Explain this difference in terms of the internal structure of each material. [1]

A light sensor uses a fixed resistor of 4.7 k\(\Omega\) in series with a light-dependent resistor (LDR) across a 6.0 V supply of negligible internal resistance. The output voltage is taken across the LDR.

(a) In room light the output voltage is 2.0 V. Calculate the resistance of the LDR. [1.5]

(b) The room is darkened. State and explain the change in the output voltage. [1]

A greenhouse controller uses a potential divider to monitor temperature. A 5.0 V supply of negligible internal resistance is connected across a fixed resistor of resistance 4.7 k\(\Omega\) in series with an NTC thermistor. The output voltage \(V_{out}\) is taken across the fixed resistor.

(a) At 20 \(^\circ\)C the thermistor has resistance 6.8 k\(\Omega\).
(i) Calculate \(V_{out}\) at 20 \(^\circ\)C. [2]
Answer = ..... V
(ii) At 35 \(^\circ\)C the thermistor resistance is 3.1 k\(\Omega\). Show that \(V_{out}\) is about 3.0 V. [1]

(b) Explain, in terms of charge carriers, why \(V_{out}\) increases as the temperature rises. [2]

(c) A heating element is made from a uniform nichrome wire of length 1.50 m and diameter 0.20 mm. The resistivity of nichrome is \(1.1\times10^{-6}\ \Omega\,\mathrm{m}\). Calculate the resistance of the wire. [3]
Answer = ..... \(\Omega\)

On a horizontal track a trolley of mass 0.80 kg moving at 0.60 m s\(^{-1}\) collides with a stationary trolley of mass 0.40 kg. The trolleys stick together and move off along the track.

(a) State the principle of conservation of momentum. [1]

(b) Calculate the speed of the joined trolleys just after the collision. [2]
Answer = ..... m s\(^{-1}\)

(c) Calculate the kinetic energy lost in the collision and state what this shows about the type of collision. [2]

(d) The joined trolleys then slow uniformly to rest over a distance of 0.25 m because of friction. Calculate the frictional force. [2]
Answer = ..... N

(e) The collision lasts 0.050 s. Calculate the mean force exerted on the 0.40 kg trolley during the collision. [1]
Answer = ..... N

A student measures the acceleration of free fall by dropping a steel ball through different heights \(h\) and timing the fall \(t\) with a light gate and data-logger. Results:

| h / m | 0.400 | 0.600 | 0.800 | 1.000 | 1.200 |
| t / s | 0.286 | 0.350 | 0.404 | 0.452 | 0.495 |
| t\(^2\) / s\(^2\) | 0.0818 | 0.1225 | 0.1632 | | 0.2450 |

(a) Calculate the missing value of \(t^2\) for \(h=1.000\) m. [1]

(b) The student plots a graph of \(h\) against \(t^2\). Explain why this should be a straight line through the origin and state what the gradient represents. [2]

(c) Use the first and last points in the table to determine the gradient, and hence a value for \(g\). [2]
Answer = ..... m s\(^{-2}\)

(d) For the \(h = 0.400\) m drop, \(h\) has an uncertainty of \(\pm0.005\) m and \(t\) an uncertainty of \(\pm0.002\) s. Using \(g=2h/t^2\), calculate the percentage uncertainty in \(g\) for this drop and the absolute uncertainty. [2]

(e) Using your answer to (c) and the data given, state whether the results are consistent with \(g=9.81\ \mathrm{m\,s^{-2}}\) and justify your answer. [1]

A digital camera has a thin converging lens of focal length 50 mm and an image sensor of 4000 \(\times\) 3000 pixels.

(a) The camera photographs a person standing 2.0 m from the lens.
(i) Calculate the distance from the lens to the sensor needed for a sharp image. [2]
Answer = ..... mm
(ii) Calculate the magnification. [1]
(iii) State the power of the lens. [1]

(b) Each pixel is stored using 12 bits. Calculate the number of bytes needed to store one uncompressed image. Give your answer in standard form. [2]
Answer = ..... bytes

(c) The camera also records sound containing frequencies up to 15 kHz.
(i) State the minimum sampling rate needed to digitise this sound without loss of information. [1]
(ii) The sound is actually sampled at 44.1 kHz using 16 bits per sample. Calculate the transmission rate in kbit s\(^{-1}\) for one channel. [1]

A student determines the resistivity of a constantan wire. The wire is 1.000 m long and is connected in a circuit with a cell, an ammeter and a voltmeter connected across the wire. The potential difference across the wire is 1.20 V when the current is 0.150 A. A micrometer screw gauge is used to measure the diameter of the wire.

(a) Describe how the student should use the micrometer to obtain a reliable value for the mean diameter of the wire. [2]

(b) The mean diameter is 0.28 mm.
(i) Calculate the resistivity of the constantan. [3]

Answer = ..... \(\Omega\) m

(ii) The uncertainty in the diameter is \(\pm 0.01\) mm. The percentage uncertainties in the resistance and in the length are 1% and 0.2% respectively. Calculate the percentage uncertainty in the resistivity and state the resistivity with its absolute uncertainty. [2]

A student tests conservation of momentum using two trolleys on a level runway. A 0.050 m long card on trolley A (mass 0.50 kg) passes through a light gate before the collision. Trolley A then hits stationary trolley B (mass 0.75 kg) and they couple together. The card on the coupled trolleys passes through a second light gate after the collision.

Time for the card to pass the first gate = 0.040 s
Time for the card to pass the second gate = 0.103 s
Each time has an uncertainty of \(\pm 0.001\) s.

(a) Calculate the velocity of trolley A before the collision. [1]

(b) Calculate the total momentum before and after the collision. [2]

(c) Determine whether the results are consistent with conservation of momentum, taking the uncertainties in the times into account. [2]

(d) Suggest one change to the apparatus which would reduce the difference between the two momenta. [1]

A student investigates a thin converging lens by placing an illuminated object at different distances from it and finding the position of a sharp real image on a screen. The Cartesian convention is used, so the object distance u is negative. The thin-lens equation is \(\frac{1}{v}=\frac{1}{u}+\frac{1}{f}\).

u / m: -0.250, -0.300, -0.400
v / m: 0.165, 0.152, 0.133

(a) Calculate 1/u and 1/v, in \(\text{m}^{-1}\), for the first pair of readings (u = -0.250 m, v = 0.165 m). [1]

(b) The student plots a graph of 1/v (y-axis) against 1/u (x-axis). Explain why the graph should be a straight line and state the gradient and the y-intercept it should have. [2]

(c) Use the second pair of readings (u = -0.300 m, v = 0.152 m) to calculate the focal length of the lens. [2]

Answer = ..... m

(d) The student finds it hard to judge the exact screen position at which the image is sharp. Suggest one way to reduce the effect of this on the value of v. [1]

A student measures the e.m.f. \(\varepsilon\) and internal resistance r of a cell. A variable resistor is connected across the cell, a voltmeter measures the terminal potential difference V and an ammeter measures the current I.

I / A: 0.10, 0.20, 0.30, 0.40, 0.50
V / V: 1.44, 1.38, 1.31, 1.26, 1.20

The terminal potential difference is related to the current by \(V = \varepsilon - Ir\).

(a) The student plots V against I. State what the gradient and the y-intercept of the graph represent. [2]

(b) Using the first and last data points as a best-fit line, calculate r and \(\varepsilon\). [3]

r = ..... \(\Omega\) \(\varepsilon\) = ..... V

(c) Calculate the power dissipated inside the cell when the current is 0.50 A. [1]

(d) The student switches off the circuit between readings. Explain why this improves the results. [1]

A student investigates a resistance wire of length \(1.000\) m. The length is measured with a metre rule with an uncertainty of \(\pm 1\) mm. The resistance of the wire is measured with a digital meter as \(2.65\ \Omega\) with an uncertainty of \(\pm 0.05\ \Omega\).

The diameter of the wire is measured at five different positions using a micrometer screw gauge. The readings are:

\(0.42\) mm, \(0.43\) mm, \(0.41\) mm, \(0.42\) mm, \(0.44\) mm

(a) (i) Calculate the mean diameter of the wire and estimate its absolute uncertainty from the spread of the readings.

Mean diameter = ..... mm
Uncertainty = ± ..... mm [2]

(ii) Calculate the percentage uncertainty in the mean diameter. [1]

(b) (i) Calculate the resistivity \(\rho\) of the wire material, using \(R = \rho L / A\).

\(\rho\) = ..... \(\Omega\) m [2]

(ii) Determine the percentage uncertainty in \(\rho\) and write the resistivity in the form \(\rho \pm \Delta\rho\). [2]

(iii) State which measurement is the largest source of uncertainty in \(\rho\) and give a reason. [1]

(c) The student now designs a heating resistor of resistance \(12.0\ \Omega\) from a different alloy wire of resistivity \(4.9 \times 10^{-7}\ \Omega\) m and diameter \(0.40\) mm.

(i) Calculate the length of wire required. [2]

(ii) The wire can safely dissipate no more than \(5.0\) W for each metre of its length. Calculate the maximum current the resistor can carry. [2]

(iii) The wire supplied is actually \(0.39\) mm in diameter. Explain whether the resistance of the finished resistor will be greater or smaller than \(12.0\ \Omega\). [1]

A greenhouse monitor uses a negative temperature coefficient (NTC) thermistor in a potential divider. The thermistor is connected in series with a fixed resistor \(R\) across a \(5.0\) V supply of negligible internal resistance. The output voltage \(V_{out}\) is taken across the fixed resistor. The resistance of the thermistor is \(4.7\ \text{k}\Omega\) at \(20\ ^\circ\)C and \(0.90\ \text{k}\Omega\) at \(60\ ^\circ\)C.

(a) Explain, in terms of charge carriers, why the resistance of the thermistor decreases as its temperature rises. [2]

(b) The fixed resistor has \(R = 2.2\ \text{k}\Omega\).

(i) Show that \(V_{out}\) is about \(1.6\) V at \(20\ ^\circ\)C. [2]

(ii) Calculate \(V_{out}\) at \(60\ ^\circ\)C.

\(V_{out}\) = ..... V [1]

(c) A voltmeter of resistance \(10\ \text{k}\Omega\) is connected across the fixed resistor \(R = 2.2\ \text{k}\Omega\) while the thermistor is at \(20\ ^\circ\)C. Calculate the reading on the voltmeter. [2]

*(d) The monitor must give the largest possible change in \(V_{out}\) between \(20\ ^\circ\)C and \(60\ ^\circ\)C. A technician has fixed resistors of \(220\ \Omega\), \(2.2\ \text{k}\Omega\) and \(22\ \text{k}\Omega\). The output will be read by the \(10\ \text{k}\Omega\) voltmeter.

Discuss which resistor is most suitable. You may include calculations in your answer. [6]

A greenhouse over-temperature warning unit uses the circuit described below (not to scale). A 6.0 V supply of negligible internal resistance is connected across a negative temperature coefficient (NTC) thermistor in series with a fixed resistor of resistance 6.8 k\(\Omega\). The output voltage \(V_{out}\) is taken across the fixed resistor and is connected to a switching circuit that sounds a buzzer when \(V_{out}\) rises above 3.0 V.

The resistance of the thermistor was measured at four temperatures:

| Temperature / \(^\circ\)C | 4 | 18 | 22 | 30 |
|---|---|---|---|---|
| Resistance of thermistor / k\(\Omega\) | 15.0 | 7.5 | 6.2 | 4.0 |

The grower wants the buzzer to sound at a temperature of about 20 \(^\circ\)C, and asks whether the unit will do this.

*Explain how the circuit responds to a rise in temperature and use the data to judge whether the buzzer will sound at about 20 \(^\circ\)C. Include calculations in your answer. Then explain how the unit could be modified so that the buzzer sounds at a higher temperature, without changing the supply or the thermistor. [6]*

A student investigates the motion of a dynamics trolley of mass \(0.50\,\text{kg}\) on a horizontal, friction-compensated track. A constant horizontal force from a pulley-and-string system gives a constant resultant force of \(0.35\,\text{N}\) on the trolley, which starts from rest. The student models the motion in discrete time steps of \(\Delta t = 0.50\,\text{s}\). In the model, the velocity at the start of each step is used to find the displacement in that step: \(\Delta s = v\,\Delta t\), and the velocity at the end of the step is \(v + a\,\Delta t\).

(a) Calculate the acceleration of the trolley. [2]

Answer = ........................ m s\(^{-2}\)

(b) Complete the iterative table. The rows for \(t = 0\), \(0.50\,\text{s}\) and \(1.00\,\text{s}\) are already complete. [4]

| t / s | v / m s\(^{-1}\) | displacement s / m |
|---|---|---|
| 0.00 | 0.00 | 0.000 |
| 0.50 | 0.35 | 0.000 |
| 1.00 | 0.70 | 0.175 |
| 1.50 | ........ | ........ |
| 2.00 | ........ | ........ |

(c) (i) Use an equation of uniformly accelerated motion to calculate the exact displacement at \(t = 2.00\,\text{s}\), and hence the percentage difference between the model and the exact value. [2]

Answer = ........................ %

(ii) Explain why the model gives a displacement that is too small, and state one change that would make it more accurate. [2]

(d) To check the speed at \(t = 2.00\,\text{s}\), the student fits a card of length \(100\,\text{mm} \pm 1\,\text{mm}\) to the trolley. A light gate records the card taking \(0.071\,\text{s} \pm 0.001\,\text{s}\) to pass. Calculate the average speed of the trolley while the card passes the gate, and the percentage uncertainty in this speed. [2]

Answer = ........................ m s\(^{-1}\) \(\pm\) ........................ %

(e)* A second student proposes a different method: using a hand-held stopwatch to time the trolley over the \(1.40\,\text{m}\) it travels from rest, and then using \(v = 2s/t\) to find the final speed. The student's reaction-time uncertainty is about \(0.2\,\text{s}\).

Compare the suitability of the two methods (light gate with card, and stopwatch) for testing the predicted speed of the trolley. You may include calculations in your answer. Reach a reasoned conclusion. [6]

*A rescue sled of mass \(1.5\,\text{kg}\) (a small model used in a lab test) is released from rest on a level, frictionless ice surface. A constant horizontal resultant force of \(6.0\,\text{N}\) acts on it.

A student models the motion in discrete time steps of \(\Delta t = 0.50\,\text{s}\). In each step the model uses the velocity at the START of the step to find the change in displacement:
\(\Delta s = v_{\text{start}}\,\Delta t\) and \(\Delta v = a\,\Delta t\).

Part of the iterative table is shown.

| t / s | a / m s\(^{-2}\) | v / m s\(^{-1}\) | s / m |
|---|---|---|---|
| 0 | 4.0 | 0 | 0 |
| 0.50 | 4.0 | 2.0 | 0 |
| 1.00 | 4.0 | 4.0 | 1.0 |
| 1.50 | | | |
| 2.00 | | | |

The student also calculates the displacement at each time using the equation \(s = ut + \tfrac{1}{2}at^2\).

Compare the results of the iterative model with those of the equation of motion. In your answer you should:
- complete the table for \(t = 1.50\,\text{s}\) and \(t = 2.00\,\text{s}\),
- calculate the displacement at \(t = 2.00\,\text{s}\) from the equation and find the percentage difference from the model,
- explain the reason for the difference, and suggest and justify one change that would make the model agree more closely with the equation.

[6]