| Aim | To determine the resistance of a galvanometer by a half-deflection method and to find its figure of merit. |
| Apparatus Required | A battery A Weston type galvanometer Two one-way keys Rheostat Screw gauge Metre-scale Ammeter Connecting wires A piece of sandpaper Two resistance boxes |
| Theory | A galvanometer is an instrument used for detecting and measuring small electric currents. It is based on the principle of the magnetic effect of current. The resistance of a galvanometer is very small, typically in the range of a few ohms, which makes it unsuitable for direct use in most electrical circuits. Therefore, a shunt resistor is connected in parallel with the galvanometer to increase its range. The resistance of the galvanometer can be determined using the half-deflection method. In this method, a known voltage is applied across the galvanometer and a shunt resistor in parallel. The current passing through the galvanometer produces a deflection on the scale. The voltage is then reduced until the deflection is halved, and the corresponding voltage and current are noted. From these values, the resistance of the galvanometer can be calculated. The figure of merit of a galvanometer is defined as the current required to produce a unit deflection on the scale. It is given by the ratio of the current passing through the galvanometer to the deflection produced on the scale. |
| Procedure | Connect the galvanometer in series with a known resistance R and a battery of known voltage V, as shown in the figure. Connect a shunt resistor S in parallel with the galvanometer, as shown in the figure. Note the deflection on the scale produced by the current passing through the galvanometer. Adjust the voltage across the circuit until the deflection is halved. Note the voltage V1 and the current I1 passing through the circuit. Calculate the resistance of the galvanometer using the formula: RG = (V-V1)/(I1-S) where RG is the resistance of the galvanometer, V is the voltage of the battery, and S is the value of the shunt resistor. Calculate the figure of merit of the galvanometer using the formula: M = I1/d where I1 is the current passing through the galvanometer, and d is the deflection produced on the scale. |
| Observation and Result | Observation: Let V = voltage of the battery Let R = resistance in series with galvanometer Let S = shunt resistance Let V1 = voltage across the shunt resistor Let I1 = current passing through the circuit The value of R is known. Voltage of the battery, V = ____V Resistance in series, R = ____Ω Shunt resistance, S = ____Ω Deflection produced on the scale, d = ____divisions Voltage across the shunt resistor, V1 = ____V Current passing through the circuit, I1 = ____A Calculation: Resistance of the galvanometer, RG = (V – V1)/(I1 – S) Figure of merit of the galvanometer, M = I1/d Result: The resistance of the galvanometer is ________ Ω, and its figure of merit is ________ A/div. |
