Question

Explain the principle, construction, and derive the current sensitivity of a moving coil galvanometer.

Hint:

Key results: - Torque on coil: \( \tau = NBAI \) - Current sensitivity: \( \frac{\theta}{I} = \frac{NBA}{k} \) - Radial magnetic field ensures linear scale and high sensitivity.

Answer 1

Concept: A moving coil galvanometer is a sensitive instrument used to detect and measure small electric currents. It works on the principle that a current-carrying conductor placed in a magnetic field experiences a torque.
Principle: When a current-carrying coil is placed in a uniform magnetic field, it experiences a torque given by: \[ \tau = N B I A \sin\theta \] In a galvanometer, the magnetic field is radial, so \( \sin\theta = 1 \): \[ \tau = NBAI \] This torque causes rotation of the coil, producing deflection proportional to current.
Construction: A moving coil galvanometer consists of the following parts:

• 
  Coil: Rectangular coil of fine insulated copper wire with many turns.
• 
  Magnet: Strong horseshoe magnet providing a radial magnetic field.
• 
  Soft Iron Core: Cylindrical core placed inside the coil to make field radial and increase sensitivity.
• 
  Suspension System: Coil is suspended using phosphor-bronze strip or springs.
• 
  Mirror/Pointer: Attached to coil to measure angular deflection.
• 
  Scale: Calibrated to read deflection.

The radial field ensures linear scale (deflection proportional to current).
Working: When current flows through the coil:

• Magnetic torque rotates the coil.
• Suspension fiber provides restoring torque.
• Coil stops when both torques balance.

Derivation of Current Sensitivity Let:

• \( N \) = number of turns
• \( B \) = magnetic field
• \( A \) = area of coil
• \( I \) = current
• \( k \) = torsional constant of suspension wire
• \( \theta \) = angular deflection

Step 1: Magnetic Torque \[ \tau_m = NBAI \]
Step 2: Restoring Torque When the coil rotates, suspension wire twists and produces restoring torque: \[ \tau_r = k\theta \]
Step 3: Equilibrium Condition At steady deflection: \[ \tau_m = \tau_r \] \[ NBAI = k\theta \]
Step 4: Current Sensitivity Current sensitivity is defined as deflection per unit current: \[ \text{Current Sensitivity} = \frac{\theta}{I} \] From above equation: \[ \theta = \frac{NBA}{k} I \] \[ \boxed{\frac{\theta}{I} = \frac{NBA}{k}} \]
Factors Affecting Sensitivity: Sensitivity increases when:

• Number of turns \( N \) increases
• Magnetic field \( B \) is strong
• Coil area \( A \) is large
• Torsional constant \( k \) is small

Voltage Sensitivity: Sometimes defined as: \[ \frac{\theta}{V} = \frac{NBA}{kR} \] where \( R \) is resistance of galvanometer.
Applications:

• Detect small currents
• Used in ammeters and voltmeters (after modification)
• Null detection in bridge circuits