To determine resistance of a galvanometer by half deflection

University
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to determine resistance of a galvanometer by half deflection

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How to Determine the Resistance of a Galvanometer by Half-Deflection Method?

Answer:

Introduction to the Half-Deflection Method

The half-deflection method is a practical approach to measuring the resistance of a galvanometer. A galvanometer is an instrument used for detecting and measuring electric current. Determining its resistance is crucial for its calibration and accurate current measurements.

Step 1: Understanding the Concept

The idea behind the half-deflection method is to first measure the full-scale deflection current and then introduce an additional resistance in parallel with the galvanometer, reducing its deflection to half. This setup allows for calculation of the galvanometer’s internal resistance using Ohm’s Law and principles of parallel circuits.

Step 2: Setting Up the Experiment

  1. Components Needed

    • A galvanometer.
    • A variable resistor or rheostat.
    • A battery or DC power supply.
    • A known resistor (often called a shunt resistor).

  2. Circuit Configuration

    • Connect the galvanometer in series with the known resistor and the variable resistor.
    • The battery or DC power supply is connected to this series combination.

  3. Initial Full-Scale Deflection

    • Adjust the variable resistor until the galvanometer needle reaches a full-scale deflection.

Step 3: Achieving Half-Deflection

  1. Introduce the Parallel Resistor

    • Connect a known shunt resistor in parallel with the galvanometer. This shunt diverts some of the current, causing the deflection to reduce.

  2. Adjust for Half Deflection

    • Again vary the resistance in the circuit (possibly by adjusting the variable resistor) until the galvanometer needle shows exactly half of the initial full-scale deflection.

Step 4: Calculating the Galvanometer’s Resistance

  1. Current Calculation

    • Let the total current in the circuit for full-scale deflection be I.
    • When the deflection is half, because of the shunt, the current through the galvanometer is halved, i.e., I/2.

  2. Formula Deduction

    • Let’s denote:
      • ( R_G ): Resistance of the galvanometer.
      • ( R_S ): Resistance of the shunt.
      • ( I_G ): Initial full-scale deflection current through the galvanometer.

    Using the principle of parallel circuits, the relationship is:

    I_G \times R_G = \left( \frac{I_G}{2} \right) \times \left( R_G \parallel R_S \right)

    Solving this equation, you can find the value of ( R_G ) using:

    R_G = R_S

    when Rs is set such that it is appropriate for the experiment.

Step 5: Verification

Repeat the experiment several times to ensure consistency in the measurements and calculations, confirming the accuracy and reliability of the determined resistance value of the galvanometer.

Final Answer:

The half-deflection method involves using a parallel shunt resistor to reduce the deflection of a galvanometer by half, allowing the calculation of the galvanometer’s internal resistance. By setting up the circuit correctly and applying knowledge of circuit principles, ( R_G ), the resistance of the galvanometer, can be effectively determined.