Resistance of a galvanometer EM 08 PDF

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Department of Engineering Technology University of Ruhuna ENT 1221: Common Practical III (Electricity and Magnetism) Experiment 8: Resistance of a Galvanometer

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

Apparatus and material required: A moving coil galvanometer, Power supply, one resistance box (RBOX1) of range 0 - 10 kΩ, one resistance box (RBO2) of range 0 - 200 Ω, two one way keys, connecting wires, multimeter

Background Theory: Galvanometer

Figure 1: Diagrams of moving coil galvanometer Galvanometer is a sensitive device used to detect very low current in a circuit of the order of 100mA. 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. The deflection of the coil is determined by a pointer attached to it, moving on the scale.

1

When a coil carrying current I is placed in a radial magnetic field, the coil experiences a deflection which is related to I as; I = kθ --------------- (1) Where k is a constant of proportionality and is termed as figure of merit of the galvanometer. The figure of merit of a galvanometer is the current required to produce a deflection of Figure 2: Circuit for finding resistance of galvanometer

one division in the galvanometer scale.

The circuit arrangement required for finding the resistance G of the galvanometer by half deflection method is shown in Fig. 2. When the switch K2 is kept open, a resistance R is introduced in the circuit, the current Ig flowing through it is given by;

Ig =

E

R+G

--------------- (2)

Here E is the emf of battery, G is the resistance of the galvanometer whose resistance is to be determined. If the current Ig produces a deflection θ in the galvanometer, then from equation (1) we get; Ig = kθ ----------------- (3) Combining equations (2) and (3) we get; E

R+G

= kθ ----------------- (4)

For measuring current of the order of an ampere, a low resistance called shunt resistance S is connected in parallel across the galvanometer having resistance G. On keeping both the switches K1 and K2 closed and by adjusting the value of shunt resistance S, the deflection of the galvanometer needle becomes

1 (half). As G and S are in parallel combination and R 2

in series with it, the total resistance of the circuit; R′ = R +

GS

G+S

-------------- (5)

2

The total current, I due to the emf E in the circuit is given by; E

I=

----------------- (6)

GS

R+ G+S

If Ig′ is the current through the galvanometer of resistance G, then; GIg′ = S(I − I′g)

Or

IS -------------------- (7) G+S

Ig′ =

Substituting the value of I from Equation (6), in equation (7) the current Ig′ is given by

Ig′ =

IS

G+S

E

=

R+

ES

Ig′ =

S

. G+S

GS G+S

R(G+S)+GS

---------------- (8)

For galvanometer current Ig′ , if the deflection through the galvanometer is reduced to half of its initial θ value = then; 2 θ

Ig′ = k ( ) = 2

ES

R(G+S)+GS

On dividing Eq. (2) by Eq. (8); Ig

Ig′

Or,

=

E

R+G

×

R(G+S)+GS ES

=2

R(G + S) + GS = 2S(R + G) RG = RS + GS G(R – S) = RS

Or,

G=

RS ---------------- (9) (R−S)

By knowing the values of R and S, the galvanometer resistance G can be determined. Normally R is chosen very high (~ 10 kΩ) in comparison to S (~ 100 Ω) for which, G≫S

3

The figure of merit (k) of the galvanometer is defined as the current required for deflecting the pointer by one division. That is,

k=

I ---------------- (10) θ

For determining the figure of merit of the galvanometer the key K2 is opened in the circuit arrangement. Using Eqs. (2) and (3) the figure of merit of the galvanometer is given by; k=

1

E

θ R+G

---------------- (11)

By knowing the values of E, R, G and θ the figure of merit of the galvanometer can be calculated. Procedure: 1. Make neat and tight connections accordingly as shown in circuit diagram (Fig. 2). 2. Give high resistance value (5 k Ω) to resistance box (RBOX 1). Then close the key K1. Adjust the resistance R from this high resistance box (RBOX 1) to get full scale deflection, even in number on the galvanometer dial. Record the values of resistance, R and deflection θ. 3. Close 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. 4. 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.

5. Calculate the galvanometer resistance (G) and figure of merit (k) of galvanometer using Eqs. (9) and (11) respectively.

Readings: Emf of the battery E = ______ V Number of divisions on full scale of galvanometer = High Resistance R/(Ω)

Table 1: Resistance of galvanometer Deflection Shunt resistance S/(Ω) in the galvanometer θ/(divisions)

Half deflection in the galvanometer θ

2

1 2 3 4 5

4

/(divisions)

Data Analysis: Emf of the battery E = ______ V

Table 2: Resistance of galvanometer High Resistance R/(Ω)

Deflection in the galvanometer θ/(divisions)

RS Half deflection in G= / (𝛺) the galvanometer (R−S)

Shunt resistance S/(Ω)

θ

2

/(divisions)

K=

1 E / θ R+G

(A/divisions)

1 2 3 4 5

Mean value of G (resistance of galvanometer) = _______ Ω Mean value of k (figure of merit of galvanometer) = ________ ampere/division.

Conclusion: 1. Resistance of galvanometer by half deflection method, G = _______Ω 2. Figure of merit of galvanometer, k = _________ ampere/division

Questions: 1. How will you use a galvanometer for measuring current? 2. (a) Out of galvanometer, ammeter and voltmeter which has the highest resistance and which has the lowest? Explain. (b) Which of the two meters has lower resistance – a milliammeter or a microammeter? 3. How to convert a Galvanometer into an Ammeter and a Voltmeter? 4. What are the factors on which sensitivity of a galvanometer depends? 5. Internal resistance of the cell is taken to be zero. This implies that we have to use a freshly charged accumulator in the experiment or use a good battery eliminator. If the internal resistance is finite, how will it affect the result? 6. What sources of errors can be found in this experiment? References: https://www.youtube.com/watch?v=eqQY1zYKoog

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