Ammeter shunt design: An ammeter has 50 Ω internal resistance and a 1 mA full-scale movement. To extend measurement to 10 mA, what is the required shunt resistor RSH1 (approximate)?
Correct Answer: 5.5 Ω
Introduction / Context:A moving-coil ammeter movement can measure only a small current directly. To measure larger currents, a low-value shunt resistor is connected in parallel with the movement so that most of the current bypasses the delicate coil while maintaining the same voltage across both paths.
Given Data / Assumptions:
- Ammeter movement resistance R_m = 50 Ω.
- Movement full-scale current I_m = 1 mA.
- Desired total current I_total = 10 mA.
- Shunt current I_sh = I_total − I_m = 9 mA.
Concept / Approach:
In parallel, the voltage across the movement equals the voltage across the shunt. First find the movement voltage at full scale, then choose R_sh so that the same voltage appears when I_sh flows through the shunt: V_m = I_m * R_m and R_sh = V_m / I_sh.
Step-by-Step Solution:
Compute movement voltage: V_m = 0.001 A * 50 Ω = 0.05 V.Compute shunt resistance: R_sh = V_m / I_sh = 0.05 V / 0.009 A ≈ 5.555... Ω.Round suitably: R_sh ≈ 5.5 Ω.Thus, a shunt of about 5.5 Ω will divert 9 mA while the movement carries 1 mA.Verification / Alternative check:
Check division: At 10 mA total, 0.05 V across the meter implies 0.05 / 5.5 ≈ 9.09 mA through shunt and 0.91 mA through movement (close; with 5.56 Ω it would be exact). The approximation is acceptable.
Why Other Options Are Wrong:
50 Ω or 55 Ω would pass far too little current. 9 Ω gives incorrect splitting. 0.55 Ω is an order of magnitude too small.
Common Pitfalls:
Forgetting to use the movement voltage, or mistakenly putting the shunt in series instead of parallel.
Final Answer:
5.5 Ω