Extending the Range of a Galvanometer

Problem Statement

• A friend has a galvanometer detecting max 10 microamperes.
• She wants to use it to measure up to 10 amperes.
• Goal: Modify the galvanometer without understanding its internal workings.

Key Objective

• Ensure that when 10 amperes flows through, the galvanometer shows '10' (change the scale accordingly).
• Achieve this by making only 10 microamperes flow through the galvanometer when 10 amperes is applied.

Strategy

• Introduce a parallel path for the current.
• Ensure only 10 microamperes flows through the galvanometer; the rest flows through the parallel path.

Basic Concept

• Total Current (10A) = Current through Galvanometer (10µA) + Current through Parallel Path
• 10A - 10µA should flow through the alternate path.

Designing the Parallel Path

• Resistance in the parallel path is crucial.
• The resistance must be tuned so that the appropriate current divides between the galvanometer and the parallel path.

Key Consideration

• Ohm's Law: Voltage across the galvanometer = Voltage across the parallel path.

Formula Derivation Overview

1. Voltage across Galvanometer (Vg) = Current through Galvanometer (Ig) \ Resistance of Galvanometer (Rg)*
2. Voltage across Parallel Resistor (Vp) = Current through Resistor (Ip) \ Resistance of Resistor (R)*
3. Since Vg = Vp
4. Form the equation: 10µA \ Rg = (10A - 10µA) \ R**
5. Solve for R (Parallel Resistance).

Practical Steps

1. Find or calculate Rg (resistance of the galvanometer which may often be provided).
2. Solve for the required parallel resistance R.
3. Implement by adding a resistor with value R in parallel with the galvanometer.

Technical Note

• The added parallel resistance is called Shunt Resistance (Shunt = Alternate Path).

Why Shunt Resistance?

• To ensure most current flows through the alternate path while allowing a tiny, measurable current through the galvanometer.

Final Steps

• Package the modified galvanometer to hide the modifications.
• Your friend only sees the improved readings up to 10 amperes and pays you for your work.

Conclusion

• The method effectively extends the range of a galvanometer to measure higher currents by appropriately using shunt resistance.
• Remember the concept rather than memorizing formulas; use basic electricity principles to solve the problem.