Question Detail
Question
A galvanometer of 50 Ω gives full scale deflection with 2 mA current. To convert it into an ammeter with a range of 10 A, the shunt resistance should be:
Correct Answer
Option C is the correct answer.
Detailed Explanation
To convert a galvanometer into an ammeter, a small resistance (shunt resistance, Rs) is connected in parallel with the galvanometer.Given:Galvanometer resistance (Rg) = 50 ΩCurrent for full scale deflection of galvanometer (Ig) = 2 mA = 2 x 10-3 ADesired total ammeter range (I) = 10 AThe current through the shunt resistance (Is) will be I - Ig.Since the galvanometer and shunt are in parallel, the voltage across them is the same:Ig * Rg = Is * RsIg * Rg = (I - Ig) * RsRs = (Ig * Rg) / (I - Ig)Rs = (2 x 10-3 A * 50 Ω) / (10 A - 2 x 10-3 A)Since I >> Ig, we can approximate (I - Ig) ≈ I = 10 A.Rs ≈ (2 x 10-3 A * 50 Ω) / 10 ARs ≈ (100 x 10-3) / 10 ΩRs ≈ 10 x 10-3 Ω = 0.01 Ω
Hint
To convert a galvanometer into an ammeter, a small resistance (shunt) is connected in parallel with the galvanometer. The voltage across the galvanometer and the shunt must be equal.