Question

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

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

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 \(10^{-3} A. \)

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, \(I_A = 1 A\)

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: \(R_S = \frac{200 \cdot 10^{-3}}{1 - 10^{-3}}\)

Find the value of the shunt resistance#:

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

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).

Key concepts

Galvanometer Resistance

A galvanometer is a sensitive instrument that measures small currents. It has its own internal resistance, known as the galvanometer resistance. This resistance is crucial in determining how much current flows through the galvanometer for a given applied voltage. In many practical situations, we aim to use the galvanometer to measure larger currents without damaging it. To achieve this, we need to understand its limits. For our exercise, the galvanometer has a resistance of \(200 \Omega\), which means it inherently restricts the current that can flow through it. Its full-scale deflection occurs at \(10^{-3} \mathrm{A}\), signifying the maximum current it can handle without being modified. If the current exceeds this limit, it could damage the galvanometer, hence the need to convert it into an ammeter for higher measurements.

Shunt Resistance

To convert a galvanometer into an ammeter that measures higher currents, a shunt resistance is used. A shunt is a low resistance connected in parallel with the galvanometer. This allows most of the current to bypass the galvanometer itself. By doing so, only a small, manageable portion of the total current passes through the galvanometer, while the majority flows through the shunt.

• This setup ensures that the galvanometer remains protected from high currents that could damage it.
• In the exercise, the required shunt resistance \(R_S\) is calculated using the formula: \(R_S = \frac{R_G \cdot I_G}{I_A - I_G}\).

This formula helps in determining the optimal shunt resistance based on the galvanometer's characteristics and the maximum current to be measured, which is \(1 \mathrm{A}\) in this case. Calculating it yields approximately \(0.2004 \Omega\), leading us to the correct option.

Parallel Circuit

The concept of a parallel circuit is key to understanding how shunt resistance works with a galvanometer. In a parallel circuit, multiple paths for current flow exist. This means each component connected in parallel shares the same voltage across it. When a shunt is connected parallel to the galvanometer, it divides the total current flowing through the circuit.

• The galvanometer channels a small current corresponding to its full-scale deflection, while the shunt carries the excess current.
• This arrangement ensures precision and safety when measuring larger currents.

The parallel configuration is efficient for adapting instruments like galvanometers for various measurement requirements. It is versatile and widely used in electronic circuit design due to its ability to maintain consistent voltage across components.

Full-scale Deflection

Full-scale deflection refers to the maximum current that a measuring instrument like a galvanometer can accurately gauge. When this limit is reached, the device's pointer or indicator reaches the extreme end of its measurement scale, signaling the maximum deflection possible without damage.

• For the galvanometer in this exercise, the full-scale deflection occurs at \(10^{-3} \mathrm{A}\).
• This is a fundamental parameter as it denotes the galvanometer's innate measuring capability before modification.

Efficient conversion into an ammeter necessitates respecting this limit and using suitable modifications, like a shunt resistance, to broaden its measuring range. Understanding full-scale deflection is crucial when extending an instrument's functionality without compromising its integrity or accuracy.