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Question : 22
Total: 26
Describe the working principle of a moving coil galvanometer. Why is it necessary to use (i) a radial magnetic field and (ii) a cylindrical soft iron core in a galvanometer?
Write the expression for current sensitivity of the galvanometer.
Can a galvanometer as such be used for measuring the current? Explain.
OR
(a) Define the term 'self-inductance' and write its S.I. unit.
(b) Obtain the expression for the mutual inductance of two long co-axial solenoidsS 1 S 2 L r 1 r 2 n 1 n 2 I S 2 .
Write the expression for current sensitivity of the galvanometer.
Can a galvanometer as such be used for measuring the current? Explain.
OR
(a) Define the term 'self-inductance' and write its S.I. unit.
(b) Obtain the expression for the mutual inductance of two long co-axial solenoids
Solution:
Principle and working : A current carrying coil, placed in a uniform magnetic field, can experience a torque.
Consider a rectangular coil for which no. of turns= N i
Area of cross-section= l × b = A
Intensity of the uniform magnetic field= B
Current through the coil= I
∴ = B I l × b = B I A
ForN τ = N B I A
Restoring torque in the spring= k θ
(k =
∴ N B L A = k θ
∴ I = (
) θ
∴ I ∝ θ
The deflection of the coil is therefore, proportional to the current flowing through it.
(i) Need for a radial magnetic field:
The relation between the current (i) flowing through the galvanometer coil, and the angular deflection( φ )
φ = (
)
whereθ
ThusI ϕ θ = 90 ∘
To get a radial magnetic field, the pole pieces of the magnet, are made concave in shape. Also a soft iron cylinder is used as the core.
The soft iron core not only makes the field radial but also increases the strength of the magnetic field.
A galvanometer has low resistance and allow only a very small current. When high current is passed the coil will burn hence galvanometer as such is not used for measuring current.
(ii) We have
Current sensitivity=
= N B A ∕ k
OR
(a) Definition of self inductance and its SI unit
(b) Derivation of expression for mutual inductance
Self inductance of a coil equals the magnitude of the magnetic flux, linked with it, when a unit current flows through it.
Alternatively
Self inductance of a coil, equals the magnitude of the emf induced in it, when the current in the coil, is changing at a unit rate.
SI unit: henry / (weber/ampere) / (ohm second.)
When currentI 2 S 1
ϕ = n 1 × µ 0
× I 2 × π r 1 2
= ( µ 0
π r 1 2 ) I 2 = M 12 I 2
where M 12 = µ 0
π r 1 2
[Note : If the student derives the correct expression, without giving the diagram of two coaxial coils, full credit can be given]
Consider a rectangular coil for which no. of turns
Area of cross-section
Intensity of the uniform magnetic field
Current through the coil
For
Restoring torque in the spring
(
The deflection of the coil is therefore, proportional to the current flowing through it.
(i) Need for a radial magnetic field:
The relation between the current (i) flowing through the galvanometer coil, and the angular deflection
where
Thus
To get a radial magnetic field, the pole pieces of the magnet, are made concave in shape. Also a soft iron cylinder is used as the core.
The soft iron core not only makes the field radial but also increases the strength of the magnetic field.
A galvanometer has low resistance and allow only a very small current. When high current is passed the coil will burn hence galvanometer as such is not used for measuring current.
(ii) We have
Current sensitivity
OR
(a) Definition of self inductance and its SI unit
(b) Derivation of expression for mutual inductance
Self inductance of a coil equals the magnitude of the magnetic flux, linked with it, when a unit current flows through it.
Alternatively
Self inductance of a coil, equals the magnitude of the emf induced in it, when the current in the coil, is changing at a unit rate.
SI unit: henry / (weber/ampere) / (ohm second.)
When current
[Note : If the student derives the correct expression, without giving the diagram of two coaxial coils, full credit can be given]
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