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Lesson 7.4 • Competency 7.3Complete Lesson
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Torque on Coils & Moving-Coil Galvanometer

Torque on rectangular current loops τ = BINA sin θ, magnetic dipole moment m = NIA, moving-coil galvanometer construction (radial field, soft iron core, hairsprings), current sensitivity S_I = (BAN)/C, ammeter shunt resistance, and voltmeter multiplier resistance.

Marking a lesson complete represents finishing your study of the topic; it does not denote tested mastery.

Learning Objectives

  • Derive torque on a planar current coil τ = BINA sin θ and define magnetic dipole moment m = NIA.
  • Explain how concave pole pieces and a soft-iron cylindrical core create a radial magnetic field, ensuring θ = 90° so deflection is directly proportional to current (linear scale).
  • Calculate shunt resistor R_s = (I_g R_g)/(I - I_g) for ammeters and multiplier resistor R_m = (V/I_g) - R_g for voltmeters.

Core Theory & Concepts

When a closed loop carrying current is placed inside a magnetic field, opposite sides experience equal and opposite parallel forces. These form a mechanical couple that turns the coil until the restoring torque of a suspension spring balances it. This principle forms the core of analog galvanometers, ammeters, voltmeters, and electric motors.

Torque on a Coil

Deflecting torque: τ = B I N A sin θ, where θ is the angle between the normal to the coil and field B. Maximum torque occurs when the plane of the coil is parallel to field lines.

\tau = B I N A \sin\theta, \quad m = N I A

Ammeter Conversion (Shunt Resistor)

A low-resistance shunt R_s is connected in parallel with the meter so majority current (I - I_g) bypasses the coil: R_s = (I_g R_g) / (I - I_g).

R_s = \frac{I_g R_g}{I - I_g}

Voltmeter Conversion (Multiplier Resistor)

A high resistance R_m is wired in series so that total voltage drop V = I_g (R_g + R_m): R_m = (V / I_g) - R_g.

R_m = \frac{V}{I_g} - R_g

Common Misconceptions

Misconception

An ammeter has very high resistance and should be connected in parallel.

Physical Clarification:An ammeter must have near-zero resistance and must be connected in series with the load. Placing an ammeter in parallel creates a dangerous short circuit.

Syllabus Topic Outline

Competency 7.3
  • 1Couples and deflecting torque on rectangular current loops: τ = BINA sin θ
  • 2Magnetic dipole moment m = NIA (A m²)
  • 3Moving-coil galvanometer construction: phosphor-bronze suspension, soft iron core, radial field
  • 4Equilibrium condition BANI = Cθ and current sensitivity S_I = (BAN)/C
  • 5Conversion to Ammeter: shunt calculation and effective resistance
  • 6Conversion to Voltmeter: multiplier calculation and loading effect