Current, resistance & potential difference

Diodes are used in a variety of electrical circuits.

Sketch the current-potential difference graph for a diode.

A package containing a light emitting diode (LED) is marked

“20 mA 3.2 V to operate normally”.

A student uses a 5 V power supply of negligible internal resistance to operate the LED.

Calculate the resistance of a protective resistor required to operate the LED normally from this power supply.

At the Facility for Rare Isotope Beams (FRIB) isotopes of elements that do not occur naturally can be produced.

FRIB contains a linear accelerator. The initial section of the accelerator is shown.

Explain why the tubes get progressively longer.

A uranium atom (²³⁸₉₂U) has 80 electrons removed. The uranium ion is then accelerated between two adjacent tubes until its kinetic energy is 200 MeV per nucleon.

Calculate the accelerating potential difference.

Show that the uranium ions will reach a velocity of about 65% of the speed of light.

When a uranium ion hits a target at this speed the ion is likely to break up and produce smaller elements. One particular isotope produced in this way is⁴⁰₁₂Mg. The naturally occurring common stable isotope of magnesium is²⁴₁₂Mg. Explain why the break-up of²³⁸₉₂U is likely to produce unusual isotopes such as⁴⁰₁₂Mg.

Questions 4 and 5 refer to the information below.

Two resistors are connected in parallel and the current in one of them is 2.0 A, as shown.

4 Which of the following is the current I in ampere?

A 3.0

B 4.0

C 5.0

D 6.0

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.

Analogue ammeters were used before digital meters became widely available. The analogue ammeter shown will measure a maximum current of 1.0 mA and has a resistance of 18 Ω.

(Source: © David J. Green/Alamy Stock Photo)

The analogue ammeter can be adapted to measure a larger current by adding a resistor, known as a shunt, in parallel with the ammeter. The arrangement is shown below. The analogue ammeter is represented by the 18 Ω resistor.

The maximum current through the 18 Ω resistor remains as 1.0 mA.

Show that the shunt would need to have a resistance of about 0.01 Ω to adapt this ammeter to read up to a maximum current of 2.0 A.

A shunt of this resistance was usually made from Manganin wire.

Calculate the length of Manganin wire of radius 0.95 mm required to make this shunt.

Part of an electric circuit is shown.

What is the current shown by the ammeter?

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.

A student set up the circuit shown and measured the current I through the filament lamp for a range of values of potential difference (p.d.) V.

The student’s data is shown in the table.

Criticise the student’s recording of the data.

The student drew a graph of how current varies with p.d. She drew a straight line on the graph and claimed that the data demonstrates that the filament lamp obeys Ohm’s law because the graph is linear.

Assess the validity of the student’s statement.

Using the circuit shown the student was unable to obtain data for p.d.s less than 2.5 V.

Draw a diagram of a circuit the student could have used to enable a full range of p.d.s from 0 to 12 V to be investigated.

A volt can be defined as a

Some liquids conduct electricity. This property can be used to pump these liquids through pipes.

A short section of a rectangular pipe containing a liquid is shown in the diagram. The pipe is placed in a magnetic field of flux density B and a current I is passed through the liquid as shown.

Add an arrow to the diagram above to show the direction in which the liquid will move.

A practical demonstration of this principle used two rectangular electrodes, opposite each other on either side of the pipe, a distance of 0.60 mm apart. The dimensions of the electrodes are shown in the diagram.

The electrodes were connected to a 1.5 V cell. Salt water was pumped using a magnetic field of magnetic flux density 0.40 T.

Show that the current through the salt water is about 20 mA.

resistivity of salt water = 1.6 Ω m

Hence calculate the force on the salt water.

A student wanted to plot a graph of current against potential difference for a light emitting diode (LED). He used the circuit shown.

Add an ammeter and a voltmeter to the circuit diagram that would enable the data to be collected.

The graph of current against potential difference obtained by the student is shown.

The student wrote the following conclusion.

“The graph shows that in general the LED is not an ohmic conductor. However, for potential differences greater than +2 V, Ohm’s law is obeyed since the graph is linear in this region.”

Criticise the student’s conclusion.

The student used the LED with a 5.0 V power supply as shown in the circuit.

To be lit to normal brightness the current through the LED must be 18 mA.

Calculate the resistance of the resistor needed in the circuit.

Mass spectrometry is a technique used to separate ions based on their charge to mass ratio.

The atoms in a sample are ionised and then accelerated and formed into a fine beam. This beam is passed into a region of uniform magnetic field and the ions are deflected by different amounts according to their mass.

Analysis of mass spectrometer data shows that chlorine exists in nature as two isotopes, chlorine-35 and chlorine-37.

State what is meant by isotopes.

In a mass spectrometer, chlorine-35 ions are accelerated through a potential difference of 8.50 kV to produce an ion beam.

Show that the speed of singly ionised chlorine-35 atoms is about 2.2 × 10⁵ m s⁻¹.

mass of an ion of chlorine-35 = 34.97 u

In most mass spectrometers the ions are passed through a velocity selector, after being accelerated, to produce a beam of ions of a particular velocity. The velocity selector consists of a pair of parallel plates, across which a potential difference (p.d.) is applied to create an electric field.

In one mass spectrometer the plates are 2.5 cm apart and a p.d. of 135 V is applied.

A magnetic field is also applied to produce a force on the ions in the opposite direction to the force from the electric field. For one particular speed the ions travel in a straight line and emerge from the selector.

Add to the diagram to indicate the directions of the electric field and the magnetic field.

The magnetic flux density applied to the velocity selector is 24.5 mT.

Deduce whether this magnetic flux density is suitable to produce a beam of chlorine-35 ions of speed 2.2 × 10⁵ m s⁻¹.

After passing through the velocity selector the ion beam enters a region of uniform magnetic flux density 0.35 T with the ions travelling at right angles to the field direction.

Explain why the ions travel in a circular path.

Calculate the radius of the circular path.

The diagram shows the path of the chlorine-35 ions in the field. Chlorine-37 ions enter the magnetic field with the same velocity.

1. Add another line to the diagram to show the path of these chlorine-37 ions.

2. Explain any differences in the paths.