Electrical power and energy transfers

The Earth’s aurora is an atmospheric effect visible in the polar regions.

Electrons in the upper atmosphere initially move vertically downwards along one of the Earth’s magnetic field lines. They are accelerated by an electric field.

These electrons collide with oxygen atoms causing atomic electrons to be excited to higher energy levels. The atomic electrons then return to lower energy levels, releasing photons of green light, red light and ultraviolet.

The accelerated electrons are accelerated by electric fields parallel to the magnetic field lines.

The length of the acceleration region is 20 000 km and the electric field value is 0.2 mV / m. The electric field can be assumed to be uniform.

Calculate the kinetic energy gained by the electrons as they pass through the electric field, in joules.

State and explain the direction of the electric field required to accelerate the electrons downwards.

A simplified energy level diagram for atomic oxygen is shown below.

Determine the wavelength of the green light emitted.

Fully justify your answer.

The horizontal current closest to the Earth produces a magnetic field which can be detected at ground level.

With reference to Fig. 1.1, state and explain the direction of this magnetic field.

Suggest two ways that the horizontal current may affect the atmosphere.

A 3D printer can manufacture small objects.

Some 3D printers use polylactic acid (PLA). PLA is supplied in the form of long filaments. The 3D printer melts the PLA and builds up the shape of the desired object in layers.

The electrical supply to the heater in the printer has an e.m.f., , of 12 V. The power of the heater is 40 W.

Calculate the resistance, R, of the heater.

The specific latent heat of fusion of PLA is 9.4 × 10⁴ J kg^–1 and its melting point is 160 °C. (b)

Define specific latent heat of fusion.

Calculate the maximum mass m of PLA that the heater could melt in one minute.

Explain why the printing process is slower in practice than your answer to (ii) suggests.

High-energy X-ray photons can destroy living cells. In radiotherapy, these photons are targeted at cancer cells.

The radiation dose is the amount of energy that a patient’s body absorbs from the high-energy X-ray photons.

Fig. 6.2 shows how this dose changes with depth below the surface of the skin.

The dose initially rises with depth because the high-energy X-ray photons produce electrons and positrons as they pass through the body. These electrons and positrons are quickly absorbed, increasing the dose.

Explain why high-energy X-ray photons produce electrons and positrons as they pass through the body.

*(ii) A 3D object called a bolus is used in radiotherapy for patients with skin cancer. A bolus targets the maximum radiation dose near the surface of the skin. So using a bolus makes the radiotherapy more effective.

A bolus can be made from PLA using a 3D printer. The bolus must fit the shape of the patient’s body exactly. This shape is found beforehand by giving the patient either a CAT scan or a PET scan.

• Explain how CAT scans and PET scans work.

• Discuss the advantages and disadvantages of having a scan to produce a bolus for radiotherapy.

Compare the e.m.f. of the battery and the potential difference (p.d.) across the variable resistor in terms of energy transfers or changes.

State which physical quantity of the variable resistor is changed to alter its resistance.

A student connects up the circuit above to determine r.

The student varies R and measures the current I. The student plots a graph of against R.

1 Use the graph to determine the power dissipated in the variable resistor when

2 The e.m.f. E of the battery is 5.0 V.

Determine r from the intercept of the line with the vertical axis.

The current in a lamp is 2.0 mA. The potential difference across the lamp is 6.0 V.

What is the energy transfer in the lamp over a period of 3.0 hours?

A 0.012 J

B 0.036 J

C 2.16 J

D 130 J

Your answer

The circuit diagram of an electrical circuit is shown below.

The positive terminals of the batteries are connected together. One battery has electromotive force (e.m.f.) 4.5 V and internal resistance 0.80 . The other battery has e.m.f. 2.4 V and internal resistance 0.50 . R is a coil of insulated wire of resistance 1.2 at room temperature.

The switch S is closed.

On the diagram, draw an arrow to show the direction of the conventional current.

Calculate the current I shown by the ammeter.

The current measured by the ammeter is smaller than that calculated in (ii). This is because the temperature of R increased due to heating by the current.

Without any changes to the circuit itself, state and explain what practically can be done to make the measured current the same as the calculated current..

The potential difference across a lamp is 2.5 V. The current in the lamp is 20 mA.

What is the energy dissipated in the lamp in 3.0 hours?

A 0.050 J

B 0.15 J

C 9.0 J

D 540 J

Your answer

A light-emitting diode (LED) emits red light when it is positively biased and has a potential difference (p.d.) greater than about 1.8 V.

The energy of a photon of red light is about 1.8 eV.

Calculate the wavelength of this red light.

The LED is connected into a circuit, as shown below.

The battery has electromotive force (e.m.f.) 4.5 V and negligible internal resistance. The resistor R has resistance 150 . Assume the p.d. across the LED is 1.8 V.

The diagram below shows a circuit designed by a student.

The LED is very close to, and facing the light dependent resistor (LDR). The circuit is taken into a dark room.

The student thought that the LED would switch on. Instead, the LED was found to repeatedly switch on and off.

Explain this behaviour of the LED in this potential divider circuit.

Suggest a possible refinement so that the LED switches on permanently when taken into the dark room.

The Planck constant h is an important fundamental constant in quantum physics.

Determine the S.I. base units for h.

A researcher is investigating the de Broglie wavelength of charged particles.

The charged particles are accelerated through a potential difference V. The de Broglie wavelength of these particles is then determined by the researcher.

Each particle has mass m and charge q.

Use Fig. 19.2 to show that the p.d. across the 50 resistor is 0.50 V.

Calculate the e.m.f. E of the power supply.

The LED emits blue light of wavelength 4.7 × 10^–7 m.

Estimate the number of blue light photons emitted from the LED per second.

number of photons per second =........ s^–1

The light from the LED is incident on a metal of work function 2.3 eV.

Explain, with the help of a calculation, whether or not photoelectrons will be emitted from the surface of the metal.

This question is about a resistance wire made of nichrome.

A student is investigating a 230 V, 1.0 kW heating element. The heating element is shown in Fig. 1.2.

A length of nichrome wire is wound in a spiral groove along 18 cm of a ceramic cylinder of diameter 1.4 cm. The distance between the centres of adjacent turns of the wire is 1.5 mm.

The numbers labelling the reels of loose wire on the laboratory shelf are the imperial standard wire gauge (swg). The student wishes to find out which reel holds the same wire as that wound on the heating element of Fig. 1.2.

The book of data gives the following information:

resistivity of nichrome at operating temperature = 1.1 × 10⁻⁶ m

Show that the resistance of the nichrome wire wound on the ceramic cylinder is 53

Show that the length of wire wound on the heating element is 5.3 m.

Use the information given in (i) and (ii) to determine the swg number of the wire used as the heating element.

Fig. 18.1 shows a circuit.

The cell has e.m.f. 1.5 V. The cell and the variable power supply both have negligible internal resistance.

The e.m.f. of the power supply is set at 4.2 V. Calculate the current I in the 33 resistor.

The e.m.f. of the variable supply is now slowly decreased from 4.2 V to 0 V. Describe the effect on the current I in the 33 resistor.

* A group of students are investigating the power dissipated in a variable resistor connected across the terminals of a cell. The cell has e.m.f. 1.5 V. The students determine the power P dissipated in the variable resistor of resistance R.

Fig. 18.2 shows the data points plotted by the students on a graph of P (y-axis) against R (x-axis).

The group of students know that maximum power is dissipated in the variable resistor when R is equal to the internal resistance r of the cell.

Describe, with the help of a suitable circuit diagram, how the students may have determined P and R. Use Fig. 18.2 to estimate the internal resistance r of the cell and discuss any limitations of the data plotted by the group.

Electromagnetic radiation is incident on a negatively charged zinc plate. Electrons are emitted from the surface of the plate when a weak intensity ultraviolet source is used. Electrons are not emitted at all when an intense visible light from a lamp is used.

Explain these observations.

The maximum wavelength of the electromagnetic radiation incident on the surface of a metal which causes electrons to be emitted is 2.9 10⁻⁷ m.

Calculate the maximum kinetic energy of electrons emitted from the surface of the metal when each incident photon has energy of 5.1 eV.

* A student conducts an experiment to confirm that the uniform magnetic flux density B between the poles of a magnet is 30 mT.

A current-carrying wire of length 5.0 cm is placed perpendicular to the magnetic field.

The current I in the wire is changed and the force F experienced by the wire is measured. Fig. 22.1 shows the graph plotted by the student.

The student’s analysis is shown on the graph of Fig. 22.1 and in the space below.

F = BIL

This is just 2 mT out from the 30 mT value given by the manufacturer, so the experiment is very accurate.

Evaluate the information from Fig. 22.1 and the analysis of the data from the experiment. No further calculations are necessary.

Use Faraday’s law of electromagnetic induction to explain why the filament lamp is lit.

The primary coil has 400 turns and the secondary coil has 20 turns. The potential difference across the lamp is 12 V and it dissipates 24 W. The transformer is 100% efficient.

1. Calculate the current in the primary coil.

2. The alternating voltage supply is replaced by a battery and an open switch in series. The switch is closed. The lamp is lit for a short period of time and then remains off. Explain this observation.