Question

State the advantages and disadvantages of a moving coil galvanometer. A moving coil galvanometer (M.C.G.) has 10 turns each of length 12cm and breadth 8cm. The coil of M.C.G. carries a current of $125\mu A$ and is kept perpendicular to the uniform magnetic field of induction ${10^{( - 2)}}T$. The twist constant of phosphor bronze fibre is $12 \times {10^{( - 9)}}\,Nm/degree$. Calculate the deflection produced.

Answer 1

A moving coil galvanometer obtains current due to the relative motion of the coil and magnetic field and is used to measure unidirectional current flow. The deflection produced can be obtained by comparing the torque produced due to the magnetic field and the torque produced by the phosphor bronze fibre.

Complete step by step answer:
The advantages of a moving coil galvanometer are as follows:
-A moving coil galvanometer has very high sensitivity.
-It has very high accuracy and flexibility.
-It does not easily get affected by stray magnetic fields.The torque to weight ratio is quite high.

The disadvantages of a moving coil galvanometer as below:
-It can only measure direct current and not alternating current.
-Frequently, errors can be seen due to mechanical stress.

Now, the number of terms here is N=10, the length of coil is L=12 cm, breadth of the coil is b=8cm. Let the current in the coil$I = 125\mu A$and the magnetic field in the region $B = {10^{( - 2)}}T$, and the spring constant $k = 12 \times {10^{( - 9)}}\,Mn/degree$.
The torque on coil due to this magnetic field is given as:

$$\tau = F \times b \\\ \Rightarrow\tau = BIl \times b \\\ \Rightarrow\tau = BIA \\\$$

For N number of coils, $\tau = NBIA$. If the coil deflects through at an angle $\theta$, then the opposing torque because of the phosphor bronze fibre would be $\tau = k\theta$. Thus comparing the two torques, we obtain;

$$k\theta = NBIA \\\ \Rightarrow\theta = \dfrac{{10 \times 125 \times {{10}^{( - 6)}} \times 12 \times {{10}^{( - 2)}} \times 8 \Rightarrow\times {{10}^{( - 2)}} \times {{10}^{( - 2)}}}}{{12 \times {{10}^{( - 4)}}}} \\\ \therefore\theta = 10^\circ \\\$$

Thus the deflection produced is $\theta = 10^\circ$.

Note: Here, the torque from the moving coil galvanometer is produced due to the motion of the galvanometer, as it needs relative motion with respect to the magnetic field to produce current, according to the Faraday’s law. The torque from the phosphor bronze fibre is created due to the twisting of the fibre, causing rotational motion and hence producing torque.