State the principle of working of a galvanometer. A galvanometer of resistance G is converted into a voltmeter to measure upto V volts by connecting a resistance R1 in series with the coil. If a resistance R2 is connected in series with it then it can measure upto V/2 volts. Find the resistance, in terms of R1 and R2, required to be connected to convert it into a voltmeter that can read upto 2V. Also find the resistance G of the galvanometer in terms of R1 and R2.

Galvanometer works on the principle of torque on a coil carrying current in a magnetic field. The torque acting on the coil is proportional to the magnitude of electric current. The coil is connected to a pointer and the pointer of the galvanometer is calibrated to show correct deflection on a scale.

Let the resistance of the galvanometer be RG.
Let maximum current carrying capacity be I.
From the given data,
V = I(RG + R1)
V/2 = I(RG + R2)
From the equations,
2 = (RG + R1)/(RG + R2)
RG = R1 - 2R2

Let the resistance required to read 2V be R3
2V = I(RG + R3)
2(RG + R1) = RG + R3
R3 = RG + 2R1
R3 = 3R1 - 2R2