State the laws of Ohm and of Joule respecting electric currents, and illustrate them by numerical examples. Deduce the latter law from the former and from the definition of electric potential.

The electro-chemical equivalent of zinc is 0·00063364 grammes per coulomb; that of copper is 0·0003261. The heat of oxidation of zinc is 1313 calories per gramme; that of copper is 661 calories. Calculate from these facts the difference of potential in a cell containing zinc, copper, and an oxidising liquid. (Assume J=42 × 10⁶, and 1 volt = 10⁸ C.G.S. units.)

State the relation between potential, capacity, and charge, of an isolated electrified sphere. Suppose such a sphere to be connected to earth by a wire of very high resistance, show that it may still be maintained at a constant potential if it shrink with a certain constant velocity; and show also that the reciprocal of the velocity of diminution of its radius is proportional to the resistance of the wire.

How would you measure the magnetic moment of a magnet? Why is it more important to know the value of the magnetic moment of a magnet than to know the strength of its poles? What effect has heat upon the magnetic moment of a magnet?

Describe a modified form of galvanometer suitable for measuring rapidly-alternating currents such as those generated in the secondary circuit of an induction coil.

What is a condenser? Describe the kind of condensers used in cable-signalling, and state why these instruments are necessary in cable work.

Explain the nature of the coefficients of mutual induction and of self-induction. Show that the coefficient of mutual induction between two circuits will be of the form, where the integration has to be carried round each of the circuits whose elements respectively are ds and ds'.

Describe some form of dynamo-electric machine suitable for working incandescent lamps on a system of parallel mains.

How can the dynamo be arranged in theory so as to keep the mains at a uniform difference of potential? And how is this done in practice?

What is meant by the Peltier-effect? How do you account for the fact that the thermo-electromotive force of an iron and copper junction reverses at a temperature of about 280° C?