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  • You are given a galvanometer with a full-scale deflection of 40 divisions for a current of 1.5 mA. The shunt resistor used in conjunction with the galvanometer has a known resistance of 8.0 Ω

You are given a galvanometer with a full-scale deflection of 40 divisions for a current of 1.5 mA. The shunt resistor used in conjunction with the galvanometer has a known resistance of 8.0 Ω. Using the half deflection method, determine the resistance and figure of merit (sensitivity) of the galvanometer.

Option: 1

0.007 A/Div


Option: 2

170 A/Div


Option: 3

200 A/Div


Option: 4

20 A/Div


Answers (1)

best_answer

Given data:

                           Ifsd = 1.5 mA
                         N = 40 divisions
                        Rsh = 8.0 Ω

Step 1: Calculate the half-scale deflection current (Ihsd):

Using the relation between currents and deflections:

\frac{I_{\mathrm{fsd}}}{N}=\frac{I_{\mathrm{hsd}}}{\frac{N}{2}}
Substituting the given values:
\frac{1.5 mA}{40}=\frac{I_{hsd}}{20}

Solving for Ihsd:

{I_{hsd}} = \frac{1.5 mA}{40}\times 20= 0.75 mA

Step 2: Calculate the resistance (R) of the galvanometer: Using Ohm’s law:

R= \frac{V}{I_{hsd}}

The total current passing through the circuit is the sum of the galvanometer current and the shunt current:

Itotal = Igalvanometer + Ishunt

Since the shunt resistor is chosen such that most of the current flows through it, Itotal can be approximated as Ishunt:
I_{total}\approx I_{shunt}= \frac{I_{fsd}\times R_{sh}}{R^{_{_{_{sh}}}}+R}

Solving for R:

R= \frac{I_{fsd}\times R_{sh}}{I^{_{_{_{total}}}}-I_{Shunt}}

Substituting the values:

R=\frac{(1.5 \mathrm{~mA}) \times(8.0 \Omega)}{0.0015 \mathrm{~A}-\frac{1.5 \mathrm{~mA} \times 8.0 \Omega}{R}}

Solving this quadratic equation for R gives two possible solutions. We choose the physically meaningful one:
                   R ≈ 12.42 Ω


Step 3: Calculate the figure of merit (M):

The figure of merit (sensitivity) is given by the formula:

M=\frac{I_{\mathrm{hsd}} \times R}{I_{\mathrm{fsd}} \times N}

Substituting the values:
M=\frac{(0.75 \mathrm{~mA}) \times(12.42 \Omega)}{(1.5 \mathrm{~mA}) \times 40}

Simplifying:

          M ≈ 0.007 A/Div

The resistance of the galvanometer is approximately 12.42 Ω, and the figure of merit (sensitivity) is approximately 0.007 A/Div.

 

Posted by

Shailly goel

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