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Worsnop in his Advanced Practical Physics for Students states that

All the resistances should be 'non-inductive', for in this method it will be seen that the galvanometer is permanently connected in the circuit, and the battery takes the position in the sliding contact.

This is essential, for we must balance the resistance of the platinum at the temperature which is fixed by the surroundings, so that the current should not pass for any appreciable time and cause a heating in the spiral.

The accompanying figures are shown below. enter image description here


But I think that having inductance in the circuit is instead beneficial for the experiment because the inductance will delay the time for the current to reach its full value, preventing heating to some extent in the PRT coil. Also, when the contact is removed the current will go to zero immediately.

Question: So, who is correct?

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As you will see from the circuit diagram the resistors are used in a variation of the Wheatstone bridge arrangement.
With such an arrangement a balance point, zero current through the galvanometer, needs to be found.
This is achieved by tapping a jockey, spade ended conducting contact, along a uniform resistance wire, $A$, until the zero current position is found.

Inductance in the circuit will produce an emf in the circuit if any of the currents change which will happen when a null deflection on the galvanometer is being looked for as the jockey is removed and touched onto the resistance wire.
This would make finding the null position more difficult.

You may think that a steady reading of zero current is easy to find directly but it is easier to find the "exact" zero current position by looking for no deflection between two position either side for which there are small deflections in opposite directions.

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This appears to be from a very old book (1927?). I think that the concern was that many high-precision resistors of the era were wire-wound resistors. Such resistors, which were similar in construction to air-coil solenoids, could actually generate a significant magnetic field which, in turn, could interfere with the operation of the galvanometer (itself a sensitive device to magnetic fields which utilized a small electromagnet to measure current) and thereby create havoc during bridge circuit tuning.

So when the text you quoted said that the resistances should be "non-inductive", I think that the concern was not really the inductances of the resistors per se, but that the text was really meant as a caution to not use wire-wound resistors in the circuit because such resistors can generate significant magnetic fields that can upset the proper operation of the galvanometer.

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