A galvanometer can be converted into a voltmeter to measure upto:
(i) 'V' volts by connecting a resistance R1 in series with coil.
(ii) 'v/2' volts by connecting a resistance R2 in series with coil.
Find the resistance (R) in terms of R1 and R2 required to convert it into a voltmeter that can read upto '2V' volts.
Answers
According to the formula, R = V/Ig – G where V is the potential difference across the terminals of the voltmeter
Ig is the current in the galvanometer
G is the resistance of the galvanometer
Case 1: Resistance R1 is connected to measure voltage V
Hence, R1 = V /Ig – G ----------------Eqn (1)
Case 2: Resistance R2 is connected to measure voltage V/2
Hence, R2 = (V/2) /Ig – G --------------Eqn (2)
Eqn (1) – Eqn (2) gives R1 – R2 = 1/Ig (V-V/2) = V/2Ig
As V/2Ig = R1 – R2 substitute in Eqn (2), we get R2 = R1 – R2 – G Hence, G = R1 – 2R2
This is G in terms of R1 and R2
Case 3: Resistance R3 is connected to measure voltage 2V
Hence, R3 = (2V) /Ig – G --------------Eqn (3)
= 4(R1 – R2) – (R1 – 2R2) = 3R1 – 2R2