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  • You are conducting an experiment where you need to measure very small currents accurately. You have a galvanometer with a full-scale deflection of 50 divisions for a current of 1.0 mA. The internal

You are conducting an experiment where you need to measure very small currents accurately. You have a galvanometer with a full-scale deflection of 50 divisions for a current of 1.0 mA. The internal resistance of the galvanometer is 20 Ω. To achieve higher sensitivity, you decide to use a shunt resistor. Determine the shunt resistance required to achieve a half-scale deflection for a current of 0.2 mA.

Option: 1

160Ω


Option: 2

170Ω


Option: 3

200Ω


Option: 4

20Ω


Answers (1)

best_answer

Given data:

   Ifsd = 1.0 mA
N = 50 divisions
Ihsd = 0.2 mA
Rinternal = 20 Ω

Step 1: Calculate the shunt current (Ishunt):

Using the relation between currents and deflections:

\frac{I_{\mathrm{fsd}}}{N}=\frac{I_{\mathrm{hsd}}}{\frac{N}{2}}

Solving for Ishunt: Ishunt =

I\text { shunt }=\left(\frac{1.0 \mathrm{~mA}}{50}\right) \times \frac{50}{2}=0.5 \mathrm{~mA}

Step 2: Calculate the total current through the shunt resistor (Itotal):

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

Itotal = Igalvanometer + Ishunt

Solving for Igalvanometer:

Igalvanometer = Itotal − Ishunt

Substituting the given values:

Igalvanometer = 1.0 mA − 0.5 mA = 0.5 mA

Step 3: Calculate the voltage drop across the shunt resistor (Vshunt):

Using Ohm’s law:

V_{\text {shunt }}=I_{\text {shunt }} \times R_{\text {shunt }}

Solving for Rshunt:

R_{\text {shunt }}=\frac{V_{\text {shunt }}}{I_{\text {shunt }}}

\begin{aligned} & \text { Substituting } V_{\text {shunt }}=I_{\text {total }} \times R_{\text {internal }}: \\ & \qquad R_{\text {shunt }}=\frac{I_{\text {total }} \times R_{\text {internal }}}{I_{\text {shunt }}} \end{aligned}

Substituting the values: R_{\text {shunt }}=\frac{0.5 \mathrm{~mA} \times 20 \Omega}{0.5 \mathrm{~mA}}=20 \Omega

To achieve a half-scale deflection for a current of 0.2 mA, a shunt resistor with a resistance of 20 Ω is required.

 

 

Posted by

Shailly goel

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