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)?

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:

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