understand the use of a galvanometer in null methods

Published by Patrick Mutisya · 14 days ago

Potential Dividers – Use of a Galvanometer in Null Methods

Potential Dividers

Objective

To understand how a galvanometer is employed in null‑method measurements involving potential dividers, and to be able to set up and interpret such experiments at A‑Level (Cambridge 9702) standard.

1. Basic Principle of a Potential Divider

A potential divider consists of two resistors, \$R1\$ and \$R2\$, connected in series across a known supply voltage \$V{\text{s}}\$. The voltage across \$R2\$ is given by the well‑known divider formula:

\$\$

V{R2}=V{\text{s}}\frac{R2}{R1+R2}

\$\$

By adjusting the ratio \$R2/(R1+R_2)\$, a desired fraction of the supply voltage can be obtained.

2. Null Method Using a Galvanometer

The null method eliminates the need to measure current directly. Instead, a galvanometer is used to detect when the potential difference between two points is zero. The key steps are:

  1. Connect the series combination of \$R1\$ and \$R2\$ across the supply \$V_{\text{s}}\$.

  2. Join a second, adjustable resistor \$R_{\text{adj}}\$ in a second branch that forms a Wheatstone‑type circuit.

  3. Link the junction between \$R1\$ and \$R2\$ to the junction between \$R{\text{adj}}\$ and a known reference resistor \$R{\text{ref}}\$ via a galvanometer.

  4. Adjust \$R{\text{adj}}\$ (or \$R{\text{ref}}\$) until the galvanometer shows zero deflection – the null condition.

  5. At null, the potentials at the two junctions are equal, giving the relation:

    \$\frac{R2}{R1+R2}= \frac{R{\text{adj}}}{R{\text{adj}}+R{\text{ref}}}\$

  6. From the known values, solve for the unknown resistance or voltage.

3. Advantages of the Null Method

  • No current needs to be measured directly, reducing systematic errors.

  • Galvanometer sensitivity allows detection of very small potential differences.

  • Instrument loading is minimal because the galvanometer draws only a tiny current at null.

4. Example Calculation

Suppose \$R1=2.0\ \text{k}\Omega\$, \$R2\$ is unknown, \$V{\text{s}}=12.0\ \text{V}\$, and the null condition gives \$R{\text{adj}}=3.0\ \text{k}\Omega\$, \$R{\text{ref}}=1.0\ \text{k}\Omega\$. Find \$R2\$.

  1. From the null condition:

    \$\frac{R2}{R1+R_2}= \frac{3.0}{3.0+1.0}= \frac{3}{4}=0.75\$

  2. Cross‑multiply:

    \$R2 =0.75(R1+R_2)\$

  3. Expand and solve for \$R_2\$:

    \$R2 =0.75R1+0.75R_2\$

    \$R2-0.75R2 =0.75R_1\$

    \$0.25R2 =0.75R1\$

    \$R2 =3R1 =3\times2.0\ \text{k}\Omega =6.0\ \text{k}\Omega\$

5. Common Sources of Error

Error SourceEffect on MeasurementMitigation
Galvanometer zero driftFalse null point, leading to systematic offsetZero the galvanometer before each trial
Thermal EMF at contactsSmall spurious voltage adds to measured potentialUse symmetric connections and allow circuit to reach thermal equilibrium
Contact resistanceAlters effective resistance valuesEnsure clean, tight connections; use four‑wire techniques where possible
Supply voltage fluctuationChanges the divider ratio during measurementUse a regulated DC source or battery with low internal resistance

6. Suggested Experimental Setup

Suggested diagram: Schematic of a potential divider with a galvanometer connected between the two junctions to detect the null condition. Include \$R1\$, \$R2\$, \$R{\text{adj}}\$, \$R{\text{ref}}\$, the supply \$V_{\text{s}}\$, and the galvanometer.

7. Summary Checklist

  • Verify galvanometer zero before each measurement.

  • Confirm all resistors are within tolerance and note their nominal values.

  • Ensure the supply voltage is stable throughout the experiment.

  • Adjust the variable resistor slowly to approach the null point.

  • Record the resistance settings at null and calculate the required quantity using the divider relation.

8. Further Reading

For deeper insight into null methods and their applications in precision measurements, consult the Cambridge International A‑Level Physics textbook, chapter on “Electrical Measurements”.