Problem 1926 - JEE Physics

Question

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.

Step-by-Step Solution

Answer

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 1: 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)

Step 2: 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?

Step 3: 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?

Step 4: 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?

Step 5: 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?

Step 6: 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.

Key Concepts

Galvanometer

A galvanometer is a sensitive device that measures small electric currents. It uses a coil of wire placed within a magnetic field, which causes the coil to move when current flows through it. This movement drives a needle that indicates the magnitude of the current. Galvanometers are ideal for detecting and measuring small currents, often in the milliampere range. However, to handle larger currents, such as several amperes, modifications are necessary. By transforming a galvanometer into an ammeter for larger currents, the device becomes even more versatile without losing its sensitivity for small currents.

Shunt Resistor

A shunt resistor plays a crucial role in converting a galvanometer into an ammeter. It is a low-resistance component connected parallel to the galvanometer coil. The purpose of this resistor is to bypass most of the current around the galvanometer, allowing the device to measure larger currents without being damaged. For example, if the maximum current through the galvanometer is 4 mA, but you need to measure 6 Amps, the shunt resistor ensures only a small, manageable portion of that current goes through the delicate coil. This method keeps the galvanometer safe while expanding its measuring range effectively.

Ammeter Range

An ammeter range refers to the spectrum of current values that an ammeter can accurately measure. For a galvanometer to be used as an ammeter with a different range, modifications are needed. Originally, galvanometers are not designed for high currents. To allow it to measure high currents, like 0 to 6 Amps, one can integrate the device with a shunt resistor. This adjustment permits the galvanometer to handle a broader range of currents while still giving accurate readings. Understanding the ammeter range is fundamental because it influences how the instrument is used in various electrical circuits.

Parallel Connection

When converting a galvanometer to an ammeter, a key feature is the shunt resistor's parallel connection to the galvanometer. A parallel circuit allows multiple paths for the current to travel, which is essential for redirecting the majority of the current away from the sensitive galvanometer coil. This arrangement ensures the instrument only handles a small portion of the total current, preventing overload and potential damage. The parallel connection effectively divides the current according to the resistance values; the lower the resistance of the path, the more current it carries. Thus, the shunt resistor allows the galvanometer to accommodate a much larger current range safely.