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Chapter 13: Problem 1926

A Galvanometer coil has a resistance of \(15 \Omega\) and gives full scale deflection for a current of \(4 \mathrm{~mA}\). To convert it to an ammeter of range 0 to \(6 \mathrm{Amp}\) (a) \(10 \mathrm{~m} \Omega\) resistance is to be connected in parallel to the galvanometer. (b) \(10 \mathrm{~m} \Omega\) resistance is to be connected in series with the galvanometer. (c) \(0.1 \Omega\) resistance is to be connected in parallel to the galvanometer. (d) \(0.1 \Omega\) resistance is to be connected in series with the galvanometer.

Short Answer

Expert verified
To convert the given galvanometer into an ammeter with a range of 0 to 6 A, a \(10 \mathrm{~m} \Omega\) resistance should be connected in parallel to the galvanometer. So, the correct option is (a).

Step by step solution

01

Identify given data

We are given: - Resistance of Galvanometer coil (Rg) = 15 Ω - Full scale deflection current (Ig) = 4 mA = 0.004 A - The desired range of the ammeter = 0 to 6 A Step 2: Calculate the resistance of the shunt resistor (Rs)
02

Calculate the resistance of the shunt resistor (Rs)

Since the galvanometer is to be converted into an ammeter, we need to connect a shunt resistor (Rs) either in parallel or series to achieve the desired range of 6 A. The resistance of the shunt resistor can be found by using the formula: \(R_s = \frac{R_g \cdot I_g}{I - I_g}\) We will substitute our given values and find Rs for each option. (a) Is Rs = 10 mΩ and connected in parallel to the galvanometer?
03

Calculate for option (a)

Let's calculate Rs for a current range of 0 to 6A using the formula above: \(R_s = \frac{15 \Omega \cdot 0.004 A}{6 A - 0.004 A} = 10 \times 10^{-3} \Omega \) The calculated resistance for the shunt resistor is 10 mΩ, and it needs to be connected in parallel to the galvanometer. So option (a) is correct. (b) Is Rs = 10 mΩ and connected in series to the galvanometer?
04

Check for option (b)

Series connection won't work for this case, as it would not create the desired ammeter range. Hence, option (b) is incorrect. (c) Is Rs = 0.1 Ω and connected in parallel to the galvanometer?
05

Check for option (c)

We have already found the correct shunt resistor value in option (a). So option (c) is incorrect. (d) Is Rs = 0.1 Ω and connected in series to the galvanometer?
06

Check for option (d)

Again, a series connection is not suitable for this case. So option (d) is incorrect. #Answer# (a) 10 mΩ resistance is to be connected in parallel to the galvanometer.

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