To determine the resistance of a galvanometer by half-deflection method and to find the figure of merit | Class 12 | Physical Practical Copy | Handwritten with observations ~ Class K Notes

Aim: To determine the resistance of a galvanometer by half-deflection method and to find the figure of merit.

Principal:

Galvanometer: Galvanometer is a sensitive device used to detect very low current. Its working is based on the principle that a coil placed in a uniform magnetic field experiences a torque when an electric current is set up in it.
When a coil carrying current, I is placed in a radial magnetic field, the coil experiences a deflection θ which is related to I as k = I/θ
I = k θ [eq.1] where k is proportionality constant and is called as figure of merit of the galvanometer.

Figure of merit(k): The figure of merit (k) of the galvanometer is defined as the current required for deflecting the pointer by one division.
When a resistance R is introduced in the circuit, the current I_g flowing through it is given by (In this case, the key K₂ is kept open)
here,
I_g =

R + G

[eq.2]

E: emf of battery
G: resistance of the galvanometer

If the current I_g produces a deflection θ in the galvanometer, then

I_g = k θ

[eq.3]

By equation 2 and 3 we get:

E

R + G
= kθ On keeping both the keys K₁ and K₂ closed and on adjusting the value of shunt resistance S, the deflection of the galvanometer needle becomes half.
Since G and S are in parallel combination and R in series with it, the total resistance of the circuit is given by
R' = R +

G + S

The total current I is given by
I =

R +

G + S

[eq.4]

If I'_g is the current through the galvanometer of resistance G, then
I'_gG = S (I - I'_g)

[eq.5]

By equation [eq.4] and [eq.5] the current I'_g is given by
I'_g =

R (G + S) + GS

[eq.6]

For galvanometer current I'_g, if the deflection through the galvanometer is reduced to half of its initial value, then

I'_g = k(θ/2)
I'_g=

R + G

On dividing [eq.2] by [eq.6] we get,
R (G + S) + GS = 2S (R + G)
RG = RS + GS
G =

R - S

By knowing the values of R and S, the galvanometer resistance G can be calculated by using the above formula. Normally R is chosen very high (nearly 10 kW) in comparison to S (nearly 100 W) for which G = S

For determining the figure of merit of the galvanometer the key K₂ is opened.
the figure of merit of the galvanometer is given by
k = (1/θ)

R + G

By knowing the values of E, R, G and &theta: the figure of merit of the galvanometer can be calculated.

Procedure:

Clean the connecting wires with sandpaper and make neat and tight connections as per the circuit diagram.

06
From the high resistance box (R_{BOX 1)} remove 5 kΩ key and then close the key K₁. Adjust the resistance R from the resistance box to get full scale deflection on the galvanometer dial. Record the values of resistance, R and deflection θ.
Insert the key K₂ and keep R fixed. Adjust the value of shunt resistance S to get the deflection in the galvanometer which is exactly half of θ. Note down S. Remove plug K₂ after noting down the value of shunt resistance, S.

07

Take five sets of observations by repeating steps 2 and 3 so that θ is even number of divisions and record the observations for R, S, θ and θ/2 in tabular form.
Calculate the galvanometer resistance G and figure of merit k of galvanometer.