Galvanometer Constant: Formula, Derivation, Definition and Significance

The galvanometer constant is an important parameter of a moving coil galvanometer. It represents the amount of electric current required to produce a unit angular deflection in the instrument. It helps determine the relationship between the current flowing through the galvanometer coil and the resulting pointer deflection.

The galvanometer constant depends on the construction and magnetic properties of the instrument, including the number of turns in the coil, coil area, magnetic flux density and torsional constant of the suspension.

Understanding the galvanometer constant is useful for calculating current sensitivity, determining the figure of merit and analysing the performance of a moving coil galvanometer.

What Is the Galvanometer Constant?

The galvanometer constant is defined as the ratio of the current flowing through the coil to the angular deflection produced.

It is mathematically expressed as:

G=Iθ\boxed{G=\frac{I}{\theta}}

Where:

  • GG= galvanometer constant
  • II= current flowing through the coil (A)
  • θ\theta= angular deflection (radian)

It indicates the current required to produce one radian of deflection in the galvanometer.

A galvanometer with a smaller galvanometer constant requires less current to produce the same deflection. Therefore, it has greater current sensitivity.

Galvanometer Constant Formula

The galvanometer constant can also be determined using the physical parameters of a moving coil galvanometer.

Its formula is:

G=KNAB\boxed{G=\frac{K}{NAB}}

Where:

  • KK= torsional constant of the suspension (N m/rad)
  • NN = number of turns in the coil
  • AA = area of the coil (m²)
  • BB = magnetic flux density (T)

This formula is derived by balancing the deflecting torque and restoring torque acting on the moving coil.

Derivation of Galvanometer Constant

The working principle of a moving coil galvanometer is based on the torque experienced by a current-carrying coil placed in a magnetic field.

When current passes through the coil, the magnetic field produces a deflecting torque. The suspension produces an opposing restoring torque. At the equilibrium position, both torques become equal.

Step 1: Deflecting torque

The deflecting torque acting on the coil is given by:

τd=NIAB\tau_d=NIAB

Where:

  • NN = number of turns
  • II= current through the coil
  • AA = area of the coil
  • BB= magnetic flux density

Step 2: Restoring torque

The restoring torque developed by the suspension is proportional to the angular deflection.

τr=Kθ\tau_r=K\theta

Where KK is the torsional constant and θ\theta is the angular deflection.

Step 3: Apply the equilibrium condition

At equilibrium, the deflecting torque is equal to the restoring torque.

τd=τr\tau_d=\tau_r

Therefore,

NIAB=Kθ NIAB=K\theta

Rearranging the equation:

I=KθNABI=\frac{K\theta}{NAB}
Iθ=KNAB \frac{I}{\theta}=\frac{K}{NAB}

Since the galvanometer constant is the ratio of current to angular deflection:

G=Iθ=KNAB\boxed{G=\frac{I}{\theta}=\frac{K}{NAB}}

This is the required expression for the galvanometer constant.

Numerical Example of Galvanometer Constant

Problem: A moving coil galvanometer carries a current of 50 µA and produces an angular deflection of 0.5 radian. Calculate its galvanometer constant.

Given:

  • Current, I=50μAI=50\,\mu A
  • Angular deflection, θ=0.5 rad\theta=0.5\ rad

Formula:

G=IθG=\frac{I}{\theta}

Substituting the values:

G=50×10−60.5G=\frac{50\times10^{-6}}{0.5}
G=100×10−6G=100\times10^{-6}

Therefore,

G=100μA/rad\boxed{G=100\,\mu A/rad}

The galvanometer constant is 100 µA/rad.

Factors Affecting the Galvanometer Constant

The galvanometer constant depends on the construction and operating characteristics of the instrument.

According to the formula:

G=KNABG=\frac{K}{NAB}

The following factors influence its value:

  1. Number of turns (N): Increasing the number of turns reduces the galvanometer constant, provided other parameters remain unchanged.
  2. Area of the coil (A): A larger coil area reduces the galvanometer constant.
  3. Magnetic flux density (B): Increasing magnetic flux density reduces the galvanometer constant.
  4. Torsional constant (K): A higher torsional constant increases the galvanometer constant because greater current is required to produce the same deflection.

Galvanometer Constant in a Ballistic Galvanometer

A ballistic galvanometer is designed to measure the electric charge passing through its coil during a short-duration electrical pulse.

In this instrument, the relevant constant is commonly called the ballistic galvanometer constant or charge sensitivity, depending on the convention used.

The charge sensitivity is expressed as:

Kq=QθK_q=\frac{Q}{\theta}

Where:

  • KqK_q= charge per unit angular deflection
  • QQ= electric charge passing through the coil (C)
  • θ\theta = first angular throw (rad)

Therefore,

Q=Kqθ Q=K_q\theta

It indicates the amount of electric charge required to produce a unit initial throw.

Unlike an ordinary moving coil galvanometer, which measures small currents, a ballistic galvanometer measures the total charge passing through its coil during a short interval.

Applications of Galvanometer Constant

The galvanometer constant is useful in several electrical measurement applications:

  • Current measurement: It helps determine the current flowing through a galvanometer from its angular deflection.
  • Sensitivity calculation: It indicates how much current is required to produce a specified deflection.
  • Instrument calibration: It helps establish the relationship between the input current and the instrument reading.
  • Galvanometer design: It helps evaluate the effects of coil turns, magnetic field strength and suspension characteristics.
  • Electrical experiments: It is used in laboratory experiments involving current measurement and moving coil galvanometers.

Conclusion

The galvanometer constant represents the current required to produce a unit angular deflection in a moving coil galvanometer. Its formula is G=I/θ=K/(NAB)G=I/\theta=K/(NAB), which is obtained by balancing the magnetic deflecting torque against the restoring torque of the suspension. It is the reciprocal of angular current sensitivity. A lower galvanometer constant indicates a more sensitive instrument capable of detecting smaller currents.

Read Next:

  1. Conversion of Galvanometer into Voltmeter: Formula, Derivation and Working
  2. Conversion of Galvanometer into Ammeter – Formula, Circuit Diagram and Derivation
  3. Applications of Galvanometer
  4. Galvanometer: Definition, Working Principle, Construction and Working
  5. Sensitivity of Galvanometer: Formula, Types, Factors and Explanation
  6. Figure of Merit of a Galvanometer: Formula, Experiment and Calculation
  7. Galvanometer Resistance: Formula, Calculation and Measurement
  8. Moving Coil Galvanometer: Principle, Construction, Working, Diagram, Formula Derivation

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