Revision: Magnetic Effects of Current and Magnetism >> Torque on a Current-Loop : Moving-Coil Galvanometer Physics (Theory) ISC (Science) ISC Class 12 CISCE

The turning effect experienced by a current-carrying loop placed in a uniform magnetic field, which forms the working principle of a moving coil galvanometer (MCG), is called torque on a current loop.

The current sensitivity of a galvanometer is defined as the deflection produced in the galvanometer when a unit current flows through it.  
Mathematically, it can be given by:

I_S = `(NBA)/k`

Where k is the couple per unit twist.

Current sensitivity is defined as the deflection e per unit current.

A moving-coil galvanometer is a sensitive instrument used to detect and measure electric current, based on the principle that a current-carrying coil placed in a magnetic field experiences a deflecting torque proportional to the current.

The current sensitivity of a galvanometer is defined as the deflection produced in the galvanometer when a unit current flows through it.

“The magnetic moment of a coil is equal to the maximum torque acting on a coil when placed in a uniform magnetic field of unit strength".

Units: NIA as A-m²

The voltage sensitivity of a galvanometer is defined as the deflection produced in the galvanometer when a unit voltage is applied across its coil.

\[\mathrm{C.S.}=\frac{\theta}{I}=\frac{NBA}{C}\]

\[\mathrm{V.S.}=\frac{\theta}{V}=\frac{NBA}{CR}\]

\[\frac{\phi}{I}=\frac{NAB}{c}\]

OR

\[\frac{\phi}{I}=\frac{NAB}{k}\]

τ = Ι Α B sin θ

Vector form:

\[\vec τ\] = \[\vec m\times\vec B\]

\[\frac{\phi}{V}=\frac{NAB}{cR}\]

OR

\[\frac{\phi}{V}=\frac{NAB}{kR}\]

• Torque depends on current, magnetic field strength and area of the loop.
• For a given perimeter, a circular loop experiences maximum torque (maximum area).
• Forms the working principle of the moving coil galvanometer (MCG).

Based on the torque on the current-carrying coil in the magnetic field: \[\tau=NIAB\]

Restoring torque: \[\tau=C\theta\]

At equilibrium: \[NIAB=C\theta\]

• A galvanometer is converted into an ammeter by connecting a low resistance (shunt) in parallel with it.
• Only a small current flows through the galvanometer, and the remaining current flows through the shunt.
• Total current: \[I=I_g+I_s\]
• Ideal ammeter has very low (≈ 0) resistance.

• A galvanometer is converted into a voltmeter by connecting a high resistance in series with it.
• The scale is calibrated in volts.
• \[I_g=\frac{V}{G+R}\]

• A current-carrying loop placed in a uniform magnetic field experiences a turning effect (torque).
• Equal and opposite forces act on opposite sides of the loop, forming a couple that tends to rotate the loop.
• The forces on the remaining sides cancel each other, so the net force on the loop is zero.
• The torque depends on the loop's orientation in the magnetic field and is zero at a particular position.
• This effect is the basic principle of galvanometers and electric motors.

• An ammeter is used to measure electric current and is always connected in series in a circuit.
• An ideal ammeter has zero resistance, but a galvanometer has appreciable resistance and cannot be used directly as an ammeter.
• To convert a galvanometer into an ammeter, a low resistance shunt is connected in parallel with the galvanometer.
• The shunt allows most of the current to bypass the galvanometer, so only a small, safe current flows through the coil.
• The shunt's value depends on the ammeter's range and ensures that full-scale deflection corresponds to the desired maximum current.

• A voltmeter is used to measure potential difference and is always connected in parallel across the points of measurement.
• An ideal voltmeter has infinite resistance so that it draws no current from the circuit.
• A galvanometer is converted into a voltmeter by connecting a high resistance in series with it.
• The resistance of a voltmeter is much greater than the resistance of the galvanometer.
• The higher the voltmeter's range, the greater its resistance; a lower-range voltmeter has lower resistance.

• A moving-coil galvanometer is used to detect and measure small electric currents.
• It works on the principle that a current-carrying coil in a magnetic field experiences a torque.
• There are two types: suspended-coil (more sensitive) and pivoted-coil (Weston; more convenient).
• A radial magnetic field is used so that deflection is directly proportional to the current.
• The coil comes to rest when the deflecting torque equals the restoring torque.
• A shunt is connected in parallel to protect the galvanometer from high currents and to enable null-point measurements.