You are provided with a resistance box R, voltmeter, key, cell of e.m.f. E, constantan wire, standard resistor, RX, an ammeter, and other necessary apparatu...

(a) Experiment (variation of V and I with external resistance). First measure the e.m.f. E of the cell with a high-resistance voltmeter on open circuit. Set up the circuit with the resistance box R, the standard resistor \(R_X\), the ammeter (in series) and the voltmeter (across the appropriate element) as shown. Set \(R=1\,\Omega\), close the key and record the current I and voltage V. Repeat for \(R=2,4,6,8\,\Omega\), recording I and V each time. Tabulate the readings, then plot V (vertical) against I (horizontal).

Specimen table

The graph is a straight line; its slope s (with the sign and unit of resistance) relates to the resistances in the circuit, and the intercept gives the e.m.f. E, consistent with \(V=E-I r\).

Two precautions: open the key immediately after each reading to avoid heating and cell run-down; avoid parallax and check the meters for zero errors.

(b)(i) Advantages of connecting identical cells in parallel:

• The total internal resistance is reduced, so a larger current can be supplied.
• The cells share the load, so they last longer (greater capacity/longer life) while the e.m.f. stays that of a single cell.

(b)(ii) Factors in choosing a material for a resistor:

• Its resistivity (it should have a suitably high, stable resistivity, e.g. constantan/manganin).
• A low temperature coefficient of resistance (resistance nearly independent of temperature) and a high melting point so it is not damaged by heating.