Question

The torque on the coil remains constant irrespective of the coil's orientation during rotation due to

• A. use of soft iron core which increases the magnetic field.
• B. radial magnetic field
• C. hair spring which provides the counter torque
• D. eddy current in the iron core which causes damping
• A. increasing number of turns of the coil
• B. increasing area of coil and magnetic field strength
• C. decreasing area of coil and magnetic field strength
• D. increasing torsional constant of the hair spring
• A. \(1.0\,\text{N m}\)
• B. \(2.0\,\text{N m}\)
• C. \(0.50\,\text{N m}\)
• D. \(0.25\,\text{N m}\)
• A. \(4015\,\Omega\)
• B. \(3985\,\Omega\)
• C. \(415\,\Omega\)
• D. \(385\,\Omega\)
• A. \(0.05\,\Omega\) should be connected in series with it.
• B. \(0.05\,\Omega\) should be connected in parallel with it.
• C. \(0.01\,\Omega\) should be connected in parallel with it.
• D. \(0.01\,\Omega\) should be connected in series with it.

Answer 1

The Correct Option is B

Concept: The deflecting torque acting on a current carrying coil placed in a magnetic field is \[ \tau = NBAI\sin\theta \] where
• \(N\) = number of turns,
• \(B\) = magnetic field,
• \(A\) = area of coil,
• \(I\) = current through coil,
• \(\theta\) = angle between magnetic field and normal to the coil. In an ordinary magnetic field, the torque depends on \(\theta\). Hence the torque changes as the coil rotates.

Step 1: Understand the purpose of radial magnetic field. In a moving coil galvanometer, the pole pieces are specially shaped so that the magnetic field becomes radial. In a radial magnetic field, the plane of the coil always remains parallel to the magnetic field lines. Therefore, \[ \theta = 90^\circ \] for all positions of the coil.

Step 2: Substitute into torque equation. Since \[ \sin 90^\circ =1, \] the torque becomes \[ \tau = NBAI. \] This expression is independent of the angular position of the coil. Hence the torque remains constant during rotation.

Step 3: Analyse other options.
• Soft iron core increases magnetic field strength but does not make torque independent of orientation.
• Hair spring provides restoring torque only.
• Eddy currents provide damping and do not affect constant torque. Therefore, \[ \boxed{\text{Correct Option (B)}} \]

Answer 2

Concept: Current sensitivity is defined as the angular deflection produced per unit current. \[ S_i=\frac{\theta}{I} \] For a moving coil galvanometer, \[ NBAI=C\theta \] where \(C\) is the torsional constant of the spring. Hence, \[ \frac{\theta}{I} = \frac{NBA}{C}. \] Therefore, \[ S_i=\frac{NBA}{C}. \]

Step 1: Observe factors affecting sensitivity. Sensitivity increases when \[ N,\; B,\; A \] increase and decreases when \[ C \] increases.

Step 2: Examine options.
• Increasing area \(A\) increases sensitivity.
• Increasing magnetic field \(B\) increases sensitivity.
• Decreasing area and magnetic field decreases sensitivity.
• Increasing torsional constant decreases sensitivity. Thus the most effective choice among the given options is \[ \boxed{\text{(B)}} \]

Answer 3

Using the torque expression for a galvanometer, \[ \tau = NBAI. \] Substituting the given values, \[ \tau = 50\times0.25\times4\times10^{-3}\times5. \] \[ \tau = 50\times0.005. \] \[ \tau=0.25\,\text{N m}. \] Therefore, \[ \boxed{\tau=0.25\,\text{N m}} \] Hence, \[ \boxed{\text{Correct Option (D)}} \]

Answer 4

For converting a galvanometer into a voltmeter, \[ R=\frac{V}{I_g}-G \] where \[ V=12V, \qquad I_g=3\times10^{-3}A, \qquad G=15\Omega. \] Substituting, \[ R = \frac{12}{3\times10^{-3}} -15. \] \[ R=4000-15. \] \[ R=3985\Omega. \] Therefore, \[ \boxed{R=3985\Omega} \] Hence, \[ \boxed{\text{Correct Option (B)}} \]

Answer 5

Step 1: Use shunt resistance formula. For conversion into an ammeter, \[ S=\frac{I_gG}{I-I_g}. \] Given, \[ I_g=5\times10^{-3}A, \] \[ G=20\Omega, \] \[ I=10A. \]

Step 2: Substitute values. \[ S = \frac{(5\times10^{-3})(20)} {10-0.005}. \] \[ S = \frac{0.1}{9.995}. \] \[ S \approx0.01\Omega. \]

Step 3: Determine connection type. A shunt resistance is always connected in parallel with the galvanometer. Therefore, \[ \boxed{ S=0.01\Omega } \] connected in parallel. Hence, \[ \boxed{\text{Correct Option (C)}} \]