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Fig.shows a potentiometer with a cell of 2.0 V and internal resistance 0.40 Omegamaintaining a potential drop across the resistor wire AB. A standard cell which maintains a constant emf of 1.02 V (for very moderate currents up to 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 kOmegais put in series with it, which is shorted close to the balance point. The standard cell is then replaced by a cell of unknown emfand the balance point found similarly, turns out to be at 82.3 cm length of the wire.(a) What is the value of epsi ? (b) What purpose does the high resistance of 600 kOmegahave ? (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 anemf of 1.0 V instead of 2.0 V? (e) Would the circuit work well for determining an extremely small emf, say of the order of afew mV (such as the typical emf of a thermo-couple) ? If not, how will you modify the circuit ? |
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Answer» Solution : (a) In a potentiometer `epsi_1/epsi_2 = l_1/l_2`and in present problem with standard cell of emf `epsi_1` = 1.02 V,`l_1 = 67.3 cm` and with a cell of unknown emf `epsi`, the null point is obtained at 82.3 cm. Hence, we have `(1.02)/(epsi) = (67.3)/(82.3)` `epsi = (1.02 xx 82.3)/(67.3) = 1.25 V` (b) The high resistance of 600 k`Omega`reduces the current through the galvanometer when the jockeycontact is far away from the balance point. The galvanometer is thus protected from thedamage likely to be caused by the high current. (c) There is no effect of this high resistance on the balance point. (d) In case, the driving emf is smaller than the emf to be measured, balance point cannot be found. (e) In such a case, the balance point will be very close to the end giving a very large percentage errorin MEASUREMENT of `epsi` . If a resistance is placed in series with the wire AB such that potential drop across AB is only SLIGHTLY larger than the emf to be measured, the balance point will be found ona larger length and the percentage ERROR will be very small. |
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