In a moving coil galvanometer, the deflection of the coil is related to the electric current (i) by the relation ___

  1. i ∝ tan θ 
  2. i ∝ θ 
  3. i ∝ θ2 
  4. i ∝ √θ  

Answer (Detailed Solution Below)

Option 2 : i ∝ θ 
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Detailed Solution

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Concept:

  • Moving coil Galvanometer: It is a device that is used to measure and detect the small amount of electric charge i.e. electric current.
    •  It is the most sensitive device and used in many electrical instruments. It is the major basic component of Ammeter and Voltmeter.
  • Principle: Moving coil galvanometer is based on the fact that when a current-carrying rectangular coil is placed in a magnetic field it experiences a torque.

F1 J.K Madhu 13.05.20 D13

Explanation:

  • From above it is clear that when a current-carrying rectangular coil is placed in a magnetic field it experiences a torque.

∴ The moment of the deflecting couple (τ) = nBIA

Where n = number of turns, B = magnetic field, I = current and A = area of coil

  • When the coil deflects, the suspension wire is twisted. On account of elasticity, a restoring couple is set up in the wire. This couple is proportional to the twist.
  • If θ = the angular twist, then,
  • The moment of the restoring couple = Cθ 

Where C = restoring couple per unit twist.

At equilibrium,

⇒ Deflecting couple = Restoring couple

Hence we can write,

⇒ nBIA = Cθ

\( \Rightarrow \theta =(\frac{nBA}{C})I\)

Here, n, B, and A are constant

  • Therefore, the deflection produced in the moving coil galvanometer is directly proportional to the amount of current passing through it.
  • Hence the relation between current and deflection is i ∝ θ.
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