EMF and internal resistance

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.

A teacher demonstrates the electric field produced between two parallel metal plates. The plates are connected to a variable power supply, as shown. The power supply has a very large internal resistance and includes a voltmeter that indicates its output.

Add to the diagram to show the electric field between the two plates.

Explain why the reading on the voltmeter indicates the e.m.f. of the power supply.

The power supply output is increased until sparks are heard and are seen in the gap between the plates. Sparks form in air when the electric field strength exceeds 3.010⁶V m⁻¹ and the air becomes conducting for a short time.

Calculate the minimum potential difference across the plates for sparks to be created.

distance between parallel plates = 2.0 mm

Explain why the voltmeter reading decreases significantly whenever sparks are produced.

Electric vehicles use a direct current (d.c.) electric motor powered by a battery for propulsion. A simplified diagram of a d.c. electric motor is shown.

A split ring consists of two semi‑circular sections that are attached to a coil. The coil is labelled ABCD. Two brushes, made of carbon, rub against and make electrical contact with the split ring.

*(a) Describe how this arrangement can lead to the coil rotating.

An advert for an electric car has the following information:

• electric motor can develop up to 390 kW output power

• car achieves a velocity of 28 m s^–1 from rest in 4.0 s at maximum power

Calculate the work done by resistive forces when the car accelerates to a velocity of

mass of car = 1950 kg

A website suggests that ‘fast‑charging’ the battery in an electric vehicle can increase the internal resistance of the battery.

Explain why an increase in internal resistance of a battery is a disadvantage.

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 potential divider circuit may contain a component known as a potentiometer. One type of potentiometer consists of a track with terminals X and Y at either end. There is a sliding contact that can move along the track connected to a terminal Z as shown.

The length of the track is 115 mm and the width is 5.0 mm.

The resistance of the track between terminal X and terminal Y is 12.0 kΩ.

Calculate the thickness t of the track.

resistivity of track material = 0.49 Ω m

The potentiometer is used to monitor the displacement of a moving tool on a machine in a production line. The tool is attached to the sliding contact. The potentiometer is connected to a resistor of resistance R and a potential difference is applied as shown. The tool moves through a maximum displacement of 60 mm from end X, producing a maximum potential difference of 5.0 V between Z and X.

Show that the potential difference between X and Y is about 10 V.

Calculate the value of R.

When the circuit is assembled, using the correctly calculated resistance value and a battery of e.m.f. 12 V, it is found that the maximum output from the potentiometer is slightly less than 5.0 V.

Explain why the maximum output is slightly less than predicted.

The tool on the machine should not travel with a speed any larger than 0.8 m s⁻¹.

The graph shows how the displacement varies with time for the downward stroke of the moving tool.

Deduce whether this speed is exceeded by the moving tool.

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.

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.

A cell is connected across a resistor. After a while the internal resistance of the cell increases.

Which row of the table correctly shows the change in the current in the circuit and the change in the terminal potential difference across the cell?

A student is investigating how the internal resistance of a dry cell varies over time. She sets up the circuit shown to draw current from the cell.

The student proposes to use a data logger to monitor the terminal potential difference (p.d.) of the cell over a period of time.

State why a data logger would be suitable to collect data in this investigation.

The graph shows how the terminal p.d. varies as the chemical energy store in the cell is depleted.

Explain, using the graph, why the current drawn from the cell decreases as the chemical energy store in the cell is depleted.

Determine the internal resistance of the cell when its chemical energy store is 80% depleted. Assume that the e.m.f. of the cell remains constant at 4.0 V.