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Chapter 34: Problem 2870

A galvanometer of resistance \(200 \Omega\) gives full scale deflection for a current of \(10^{-3} \mathrm{~A}\). To convert it into an ammeter capable of measuring upto \(1 \mathrm{~A}\). What resistance should be connected in parallel with it ? (A) \(2 \times 10^{-1} \Omega\) (B) \(2 \Omega\) (C) \(2 \times 10^{-3} \Omega\) (D) \(2 \times 10^{-6} \Omega\)

Short Answer

Expert verified
The correct answer is \( (A) 2 \times 10^{-1} \Omega \), as the shunt resistance calculated to convert the galvanometer into an ammeter capable of measuring up to 1 A is approximately \( 0.2004 \Omega \).

Step by step solution

01

Understand the concept of the shunt#:

The shunt is a low resistance connected in parallel with the galvanometer that allows most of the current to pass through it. This allows the galvanometer to measure higher currents without damaging or affecting the galvanometer's measurements. In this case, we want to measure up to 1 A with a galvanometer that has a full-scale deflection current of \(10^{-3} A. \)
02

Identify the given parameters#:

We are given the following values: Galvanometer resistance, \(R_G = 200 \Omega\) Galvanometer full-scale deflection current, \(I_G = 10^{-3} A\) Maximum current to be measured, \(I_A = 1 A\)
03

Calculate the shunt resistance#:

To calculate the shunt resistance, we will use the following formula derived from the principle of parallel resistance: \(R_S = \frac{R_G \cdot I_G}{I_A - I_G}\) Substitute the given values: \(R_S = \frac{200 \cdot 10^{-3}}{1 - 10^{-3}}\)
04

Find the value of the shunt resistance#:

Now, let's calculate the value of the shunt resistance: \(R_S = \frac{200 \cdot 10^{-3}}{1 - 10^{-3}} \approx 0.2004 \Omega\)
05

Choose the correct answer from the given options#:

Since we have found the value of the shunt resistance, we can now choose the correct option. The calculated value is approximately \(0.2004 \Omega\), which is closest to option (A) \(2 \times 10^{-1} \Omega\). Therefore, the correct answer is option (A).

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Most popular questions from this chapter

A galvanometer of resistance \(200 \Omega\) gives full scale deflection with 15 milli-ampere current. In order to convert it into a \(15 \mathrm{~V}\) range voltmeter. What is the value of resistance connected in series ? (A) \(1000 \Omega\) (B) \(800 \Omega\) (C) \(2500 \Omega\) (D) \(1500 \Omega\)

One micro-ammeter has a resistance of \(100 \Omega\) and a full scale range of \(50 \mu \mathrm{A}\). ft can be used as a voltmeter or as a higher range ammeter provided a resistance is added to it. Pick the correct range and resistance combinations (s). (A) \(5 \mathrm{~mA}\) range with \(1 \Omega\) resistance in parallel (B) \(10 \mathrm{~mA}\) range with \(1 \Omega\) resistance in parallel (C) \(10 \mathrm{~V}\) range with \(200 \mathrm{k} \Omega\) resistance in series (D) \(50 \mathrm{~V}\) range with \(10 \mathrm{k} \Omega\) resistance in series

The seave of a galvanometer of resistance \(100 \mathrm{Q}\) contains 25 divisions. It gives a deflection of 1 division on passing a current of $4 \times 10^{-4} \mathrm{~A}$. The resistance in ohm to be added to it. so that it may become a voltmeter of range \(2.5 \mathrm{~V}\) is (A) 250 (B) 300 (C) 150 (D) 100

A galvanometer, having a resistance of \(50 \Omega\), gives a full scale deflection for a current of \(0.05 \mathrm{~A}\). The length in meter of a resistance wire of area of cross-section \(2.97 \times 10^{2} \mathrm{~cm}^{2}\) that can be used to convert the galvanometer into an ammeter which can read a maximum of \(5 \mathrm{~A}\) current is (specific resistance of wire $=5 \times 10^{-7} \Omega \mathrm{m}$ ) (A) \(1.5\) (B) 6 (C) 8 (D) 3

A galvanometer with resistance \(100 \Omega\) is converted into an ammeter with a resistance of \(0.1\). The galvanometer shows full scale deflection with current of \(100 \mu \mathrm{A}\). Then what will be the minimum current in the circuit for full scale deflection of galvanometer ? (A) \(0.1001 \mathrm{~mA}\) (B) \(100.1 \mathrm{~mA}\) (C) \(1000.1 \mathrm{~mA}\) (D) \(1.001 \mathrm{~mA}\)
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