Figure 3.33 shows a potentiometer with a cell of 2.0 V and internal resistance 0.40 W maintaining a potential drop across the resistor wire AB. A standard cell which maintains a constant emf of 1.02 V (for very moderate currents upto a few mA) gives a balance point at 67.3 cm length of the wire. To ensure very low currents drawn from the standard cell, a very high resistance of 600 kW is put in series with it, which is shorted close to the balance point. The standard cell is then replaced by a cell of unknown emf e and the balance point found similarly, turns out to be at 82.3 cm length of the wire. (a) What is the value e ? (b) What purpose does the high resistance of 600 kW have? (c) Is the balance point affected by this high resistance? (d) Would the method work in the above situation if the driver cell of the potentiometer had an emf of 1.0V instead of 2.0V? (e) Would the circuit work well for determining an extremely small emf, say of the order of a few mV (such as the typical emf of a thermo-couple)? If not, how will you modify the circuit?
Answers
(a) for emf of 1.02V, the balance point is 67.3 cm of wire. for unknown emf E , the balance point is 82.3 cm of wire.
so, 1.02V/E = 67.3cm/82.3cm
E = 1.02 × 82.3/67.3 V
= 1.25 V
(b) A high resistance of 600kΩ is joined in series with the cell so as to prevent the galvanometer from excessive current, when jockey is touched far from the null point. once the null point is closely known the 600kΩ is show circuited so that exact position of null point can be achieved.
(c) in presence of high resistance we will obtain null point for a longer length than a sharp position , it is because of very low current near the null point .
(d) internal resistance of the cell do not affect the balance point , as no current is drawn at null point.
(e) if the driver cell of standard circuit has an emf smaller than emf of the cell to be balanced then null point will not be achieved in the length of potentiometer wire and galvanometer will provide only one side deflection always.
(f) in the given state , the circuit will be unsuitable, as for E of the order of mV the null point will be very close to end A and percentage error in the measurements of emf will be larger.
To make suitable arrangement the potential drop in potentiometer wire is brought down to few mV, so that balance point is obtained at suitable length and this is done by introducing a high resistance in series in the standard deliberation circuit.