JEE Main 2024 · 29 January · morning · Single correct · +4 / −1
A galvanometer having coil resistance 10 Ω shows a full scale deflection for a current of 3 mA. For it to measure a current of 8 A, the value of the shunt should be:
- (a) 3.75 × 10⁻³ Ω
- (b) 3 × 10⁻³ Ω
- (c) 4.85 × 10⁻³ Ω
- (d) 2.75 × 10⁻³ Ω
Answer and solution
Answer (a) 3.75 × 10⁻³ Ω
Solution
Physics sir · 4 steps
The shunt and the coil sit in parallel, so they share the same voltage. Set the two voltages equal.
- Split the current. At full scale, only I_g = 3 mA may go through the coil. The rest, I - I_g, must go through the shunt S connected in parallel.
I_g G = (I - I_g) S ⇒ S = (I_g G)/(I - I_g)
- Put in numbers. I_g G = 3 × 10⁻³ × 10 = 0.03 V. The shunt current is 8 - 0.003 = 7.997 A.
- Solve for S. S = 0.03/7.997 = 3.75 × 10⁻³ Ω. Since I_g is tiny compared with 8 A, using 0.03/8 gives the same value.
- So. The shunt should be 3.75 × 10⁻³ Ω, which is option (a).
The idea to keep. For an ammeter, a small shunt goes in parallel with the coil. Equal voltages give S = (I_g G)/(I - I_g), and the bigger the range, the smaller the shunt.
Answer from the NTA final answer key. Solution by PrepWiser.