Question:
a galvanometer can be converted into a voltmeter to measure upto
1. V volt by connecting a resistance R1 in series
2. V/2 volt by connecting we resistance R2 in series
Find resistance R in terms of R1 & R2 to convert it into a voltmeter that can read up to 2V volt
Answer:
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
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