EMF & internal resistance

Explain what is meant by

internal resistance of a cell

e.m.f. of a cell.

A student uses the circuit below to investigate the resistivity of a wire.

The cell has e.m.f. and internal resistance r. The wire has resistivity and diameter d.

The student takes five measurements of the diameter of the wire, which are shown in the table below.

Suggest how the student made these measurements.

The student calculates the value of the diameter as d = 0.455 ± 0.005 mm.

Explain how the student calculated the value of the diameter, and its uncertainty, from the data in the table above.

The student varies the length L of the wire in the circuit and records the current I using the ammeter.

The student plots a graph of against L. The data points, error bars, line of best fit and a line of worst fit are shown in the graph below.

The cell has e.m.f. = 1.45 ± 0.05 V

The wire has diameter d = 0.455 ± 0.005 mm

1 Calculate the gradient of the best fit line and use this to determine a value for the resistivity of the wire.

You are not required to determine an uncertainty.

2 Determine a value for the internal resistance r of the cell and its absolute uncertainty.

r =........ ±........

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 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..

State Kirchhoff’s second law and the physical quantity that is conserved according to this law.

On Fig. 18.2 draw the straight line of best fit. Determine the gradient of this line.

gradient =........ A^–1 m^–1

Show that the gradient of the line is , where is the resistivity of the material of the wire, A is the area of cross-section of the wire and E is the e.m.f. of the cell.

The e.m.f. E of the cell is 1.5 V. The diameter of the wire is 0.38 mm.

Use your answer to (i) and the equation given in (ii) to determine .

=........ m

Derive the S.I. base units for resistance.

Fig. 16.1 shows the I-V characteristics of two electrical components L and R.

The component L is a filament lamp and the component R is a resistor.

Show that the resistance of R is 40 .

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.