Electrical power & energy transfers

Solar cells are being used in increasing numbers around the world.

The current I from a solar cell can be varied by connecting it to a variable resistor. The graph shows how I and the terminal potential difference V across a solar cell vary.

Complete the circuit diagram below to show how the data for the graph could be obtained.

Show that the maximum power output from the solar cell is about 2 W. You should use values from the graph.

The area of the solar cell is 104 cm².

Determine the efficiency of the solar cell when operating at maximum power.

intensity of sunlight = 1000 W m^–2

Calculate the internal resistance of the solar cell when operating at maximum power.

The potential difference (p.d.) from a power pack alternates at a frequency of 50 Hz. The root-mean-square (r.m.s.) value of the output p.d. is measured to be 8.5 V using an a.c. voltmeter.

The output from the power pack is connected to a resistor of resistance 1.5 Ω.

Show that the rate of power dissipation in the resistor is about 48 W.

A lab technician used the resistor to heat 1.25 10^–4m³ of milk in a beaker.

Calculate the time taken for the milk to increase in temperature by 12 °C.

specific heat capacity of milk = 3930 J kg^–1K^–1

The lab technician used an oscilloscope to determine the supply frequency and check the r.m.s. output p.d. displayed by the voltmeter.

Describe the methods the technician should use.

Electrical power is transmitted from Norway to Britain using a cable laid under the North Sea.

The following information is published on a website.

Deduce, by calculation, whether the claim for efficiency is correct.

A student is investigating circuits that include a filament bulb. The filament bulb is labelled ‘1.5 V, 0.50 W’.

Show that the resistance of the filament bulb when operating normally is about 5 Ω.

*(b) The student wishes to control the brightness of the filament bulb using a potentiometer. The student connects the circuit shown. The total resistance of the potentiometer is very much larger than the resistance of the filament bulb.

Explain how the brightness of the filament bulb changes as the potentiometer slider is moved from A to B.

The student connects the filament bulb in the circuit shown below. The capacitor is initially uncharged and has a capacitance of 1.2 F.

The resistance of the filament bulb is 5 Ω.

Explain how the brightness of the filament bulb will vary as the switch is closed.

*3 A student connects three identical 3 V bulbs to a 6 V battery of negligible internal resistance. The circuit includes two switches, S₁ and S₂, as shown.

The student closes S₁ and records the brightness of each bulb.

With S₁ still closed, the student closes S₂.

Explain how the brightness of bulb 1 compares with the brightness of bulb 2 before and after S₂ is closed.

The circuit shows a 1 mF capacitor connected to an a.c. supply. The graph shows how the potential difference V varies with time t.

Calculate the root‑mean‑square potential difference.

The formula used to generate this graph is V = 5 sin (100 πt)

Explain why this formula leads to the graph above.

A spreadsheet is used to model how the current I in the 1 mF capacitor varies with t. Six rows of the spreadsheet are shown below.

Explain how cell E10 has been calculated.

State the formula used to calculate cell G11.

Calculate the maximum energy stored on the capacitor.

The spreadsheet data are used to plot a graph to show how I varies with t. This is shown as a dashed line below.

The corresponding graph of V against t is also shown as a continuous line.

Deduce whether the capacitor dissipates power over one cycle of the a.c. supply.

A battery has an e.m.f. of 12 V and an internal resistance of 0.50 Ω. The battery is connected into a circuit, as shown.

Each bulb has a normal working power of 40 W when a potential difference (p.d.) of 12 V is applied.

Initially the switch is open.

Calculate the terminal p.d. of the battery when bulb 1 is lit. Assume that the resistance of the bulb has its normal working value.

Terminal p.d. of battery =_........

Explain how the brightness of bulb 1 changes when the switch is closed. No further calculations are necessary.

A student planned to vary the current in the heater from 0 A to 5 A. The student connected the following circuit to measure the current in the heater.

Criticise the student’s circuit.

The student corrected the circuit and closed the switch. He waited until the water started boiling. He started a stopwatch and recorded the readings on the balance at regular time intervals.

Sketch a graph, on the axes below, of how the readings on the balance would vary with time.

The heater was switched on for 6.0 minutes and the change in mass of water in the beaker was 7.5 g.

Calculate the specific latent heat of vaporisation of water, L.

V = 12 V I = 4.2 A

The errors in the experiment include uncertainty in the mass reading and uncertainty in reading the stopwatch, as the water boils.

Explain how another significant source of error affects the value of L obtained from the experiment.

A student drives a go‑kart up a slope.

The slope is at an angle of 5.7° to the horizontal. The go‑kart moves with a constant

Calculate the power of the go‑kart.

mass of go‑kart and driver = 60 kg resistive force on the go‑kart = 18 N

The go‑kart is powered by a battery connected to a motor. The rate of thermal energy transfer by the wiring in the motor is 55 W.

Calculate the resistance of the wiring in the motor.

current in motor = 24 A

The world solar challenge is set every two years, in Australia. The challenge is to complete a three thousand kilometre route with a vehicle powered only by the Sun.

Vehicles have their surfaces fitted with solar panels, as shown in the photograph.

(Source: © LAURENT DOUEK/LOOK AT SCIENCES/SCIENCE PHOTO LIBRARY)

One of the solar panels has an e.m.f. of 8.2 V when in sunlight. The terminal potential difference is 5.5 V when a current of 0.45 A is drawn from the solar panel.

Calculate the internal resistance of the solar panel in these conditions.

A bank of 380 of these solar panels is used to charge the battery in a vehicle. The panels are connected in parallel and the current provided by each panel is 0.45 A. When fully charged, the energy stored in the battery is 12 kW h.

Calculate the time, in hours, to fully charge this battery if the solar panels are in sunlight. Assume the efficiency of charging this battery is 100%.

The vehicle can reach a maximum speed of 34 m s⁻¹ on flat ground. The electric motor used to move the vehicle has a power of 4.5 kW.

Calculate the initial acceleration of the vehicle as it starts from rest.

mass of vehicle and driver = 420 kg

State one assumption made in this calculation.

Solar power alone would not be suitable for a family car because it is not sunny all the time.

Give two further reasons why solar power alone would not be suitable.

A student connected the output from a source of alternating potential difference (p.d.) to a series resistor combination.

She connected an oscilloscope across the 150 Ω resistor as shown.

The trace obtained on the oscilloscope is shown below.

Determine the peak p.d. across the 150 Ω resistor.

y-sensitivity of oscilloscope = 2.0 V per division

Peak p.d. across 150 Ω resistor =_........

Calculate the root mean square (r.m.s.) value of the current in the circuit.

r.m.s. value of current =_........

Calculate the power dissipated in the circuit.

Another student suggested that a voltmeter would be more accurate than using an oscilloscope to determine the magnitude of the p.d.

Comment on this suggestion.

The apparatus shown can be used to determine a value for the specific latent heat of vaporisation of water.

In one experiment the current in the heater was 8.20 A, and the potential difference across the heater was 230 V.

Show that the power of the heater was about 2 kW.

There was 0.655 kg of water in the flask at an initial temperature of 22.5 °C. The heater was switched on, and the water in the flask was heated to boiling point.

Calculate the minimum time taken for the water to be heated to 100.0 °C.

specific heat capacity of water = 4190 J kg⁻¹K⁻¹

The heater was left on and water continued to boil in the flask. The water was allowed to boil for a few minutes. The conical flask was then placed under the heat exchanger and water was collected in it.

Give a reason why the water was left boiling for a few minutes before the conical flask was put in place.

Water with a mass of 95.0 g was collected in a time of 125 s.

Calculate the rate of energy transfer in the heat exchanger.

specific latent heat of vaporisation of water = 2.26 × 10⁶J kg⁻¹

Discuss your answers to (a)(i) and (b)(ii).

State how the apparatus could be modified to minimise the effect of a significant source of error.

The properties of capacitors make them useful in timing circuits.

The following circuit is used to provide an input Y to an integrated circuit.

Initially the capacitor is uncharged. The switch S₁ is closed. Sketch a graph to show how the potential at point Y varies with time.

When the potential at Y is 8.0 V, the switch S₂ is closed.

Calculate the time taken for the potential at Y to decrease to 2.0 V.

Calculate the energy stored on the capacitor when the potential at Y is 2.0 V.

When the potential at Y is 2.0 V, the switch S₂ is opened. Calculate the power dissipated by the resistance R₁ when the potential at Y is 2.0 V.

The properties of capacitors make them useful in timing circuits.

The following circuit is used to provide an input Y to an integrated circuit.

Initially the capacitor is uncharged. The switch S₁ is closed. Sketch a graph to show how the potential at point Y varies with time.

When the potential at Y is 8.0 V, the switch S₂ is closed.

Calculate the time taken for the potential at Y to decrease to 2.0 V.

Calculate the energy stored on the capacitor when the potential at Y is 2.0 V.

When the potential at Y is 2.0 V, the switch S₂ is opened. Calculate the power dissipated by the resistance R₁ when the potential at Y is 2.0 V.

Hybrid electric vehicles (HEV) use the same device both as a generator to charge the car battery and as an electric motor to support the propulsion system. A simplified diagram of the device is shown. The coil can rotate freely around the axis.

*(a) Describe how the device can be used as both a generator and an electric motor.

The circuit diagram shows a car battery connected to an electric motor for a HEV. The battery has an electromotive force (e.m.f.) 180 V and internal resistance 0.036 Ω.

The motor has a maximum power of 88 kW.

Show that the current I drawn by the electric motor when operating at this power would be given by the equation

Solving the equation above produces an answer of I = 550 A. At maximum power, the car can accelerate from rest to sixty miles per hour in under 7 s.

The maximum charge capacity of the battery within this HEV is 6.1 amp-hour.

Deduce whether the battery could maintain this current for up to 7 s.

Hybrid electric vehicles (HEV) use the same device both as a generator to charge the car battery and as an electric motor to support the propulsion system. A simplified diagram of the device is shown. The coil can rotate freely around the axis.

*(a) Describe how the device can be used as both a generator and an electric motor.

The circuit diagram shows a car battery connected to an electric motor for a HEV. The battery has an electromotive force (e.m.f.) 180 V and internal resistance 0.036 Ω.

The motor has a maximum power of 88 kW.

Show that the current I drawn by the electric motor when operating at this power would be given by the equation

Solving the equation above produces an answer of I = 550 A. At maximum power, the car can accelerate from rest to sixty miles per hour in under 7 s.

The maximum charge capacity of the battery within this HEV is 6.1 amp-hour.

Deduce whether the battery could maintain this current for up to 7 s.

The photograph shows a statue of Buddha in Sri Lanka, which is protected by a lightning conductor.

During a storm, a potential difference of 2.7 MV was generated between a cloud and the top of the lightning conductor on the statue. A flash of lightning passed between the cloud and the lightning conductor, producing a current of 25 kA for a time of 7.5 ms.

Calculate the energy transferred by the lightning strike.

The lightning conductor is a length of copper wire with a diameter of 1.2 × 10^–2m and a resistance of 4.3 × 10⁻³ Ω. It runs along the back of the statue from the base to a height of 1.5 m above the top of the statue.

A guidebook claims that the statue is over 30 m high.

Assess the validity of this claim.

resistivity of copper = 1.7 10⁻⁸ Ω m

Give a reason why the lightning conductor should be taller than the statue.

The photograph shows a statue of Buddha in Sri Lanka, which is protected by a lightning conductor.

During a storm, a potential difference of 2.7 MV was generated between a cloud and the top of the lightning conductor on the statue. A flash of lightning passed between the cloud and the lightning conductor, producing a current of 25 kA for a time of 7.5 ms.

Calculate the energy transferred by the lightning strike.

The lightning conductor is a length of copper wire with a diameter of 1.2 × 10^–2m and a resistance of 4.3 × 10⁻³ Ω. It runs along the back of the statue from the base to a height of 1.5 m above the top of the statue.

A guidebook claims that the statue is over 30 m high.

Assess the validity of this claim.

resistivity of copper = 1.7 10⁻⁸ Ω m

Give a reason why the lightning conductor should be taller than the statue.

A student determined the latent heat of vaporisation of a liquid using an electrical heater to boil the liquid in a Pyrex beaker.

The apparatus used is shown below.

She connected the heater into a circuit and took measurements of the potential difference V and the current I for the heater.

Complete the circuit diagram to show a suitable circuit.

The student monitored the mass of the beaker and the liquid m over the time t for which the liquid was boiling. Her results are plotted on the graph.

The student used her graph to determine a value for the latent heat of the liquid in the beaker. She concluded that the liquid was pure water.

Comment on the validity of the student’s conclusion.

V = 20.5 V

I = 10.5 A

Explain how this method might be modified to improve the accuracy of the student’s conclusion.