Question

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) \(1.001 \mathrm{~mA}\)

Short answer

The minimum current in the circuit for full scale deflection of the galvanometer is \(100.1 \: mA\), which is Option (B).

Step-by-step solution

Identify the given values

The given values are: - Resistance of the galvanometer (\(G\)): 100 Ω - Resistance of the ammeter (\(R\)): 0.1 Ω - Current in the galvanometer for full scale deflection (\(I_{G}\)): 100 µA

Set up the equation

We will use the formula for converting a galvanometer into an ammeter: \(I_{A} = (G + R) \cdot I_{G}\)

Plug in the given values

Let's plug the values into the equation: \(I_{A} = (100 + 0.1) \cdot 100 \mu A\)

Solve for \(I_{A}\)

Now, let's solve the equation to find the minimum current in the circuit for full scale deflection of the galvanometer: \(I_{A} = (100.1) \cdot 100 \mu A = 10010 \mu A = 100.1 \: mA\) The minimum current in the circuit for full scale deflection of the galvanometer is 100.1 mA, which is Option (B).

Key concepts

Ohm's Law: Understanding the Basics

Ohm's Law is a fundamental principle in the field of electronics and physics. It helps us understand the relationship between voltage, current, and resistance in an electrical circuit. The law is expressed by the equation \( V = I \times R \) where \( V \) represents voltage, \( I \) is the current, and \( R \) is the resistance.
Understanding Ohm's Law is crucial because it forms the foundation for analyzing circuits, diagnosing circuit problems, and designing electronic devices. This principle allows you to calculate the amount of current that will flow through a circuit given the voltage and resistance. It is an essential tool for engineers and students alike.

• Voltage (\( V \)): The potential difference that drives current through a circuit.
• Current (\( I \)): The flow of electric charge through a circuit, measured in amperes (A).
• Resistance (\( R \)): The opposition to current flow within a circuit, measured in ohms (Ω).

By applying Ohm's Law, students can gain a deeper understanding of how circuits function, and it becomes pivotal in tasks like converting a galvanometer to an ammeter.

Full Scale Deflection Explained

Full Scale Deflection refers to the maximum current a galvanometer can accurately measure. In this state, the needle or pointer of the galvanometer completely deflects to the end of the scale.
For a galvanometer to accurately display current, it must be designed to meet specific full scale deflection requirements. This ensures the device can provide precise measurements while avoiding damage from excessive current.
In the exercise at hand, the galvanometer shows a full scale deflection at a current of \( 100 \mu A \). This means any current larger than this value can potentially harm the device or render the readings inaccurate.

Current Measurement with Converted Ammeters

Current measurement is essential for electrical and electronic circuit analysis. A galvanometer is a precision instrument initially used for measuring small currents. By adding a shunt resistor, it can be converted into an ammeter.
Once converted, the ammeter measures larger currents while protecting the galvanometer from damage. This conversion process involves connecting a small-value resistor (shunt resistor) in parallel with the galvanometer. The shunt allows most of the current to bypass the galvanometer, ensuring only a fraction of the total current passes through it.
The conversion is useful in extending the range of an existing galvanometer to measure current precisely and safely in various circuits.

Resistance Calculation in Galvanometer to Ammeter Conversion

Resistance calculation is a significant part of turning a galvanometer into an operational ammeter. To make this conversion, you need to calculate the additional resistance required to handle higher currents.
In our exercise, the galvanometer's resistance is given as \( 100 \Omega \), and the combined resistance for the ammeter is \( 0.1 \Omega \). By using the resistance values, we can determine how much current the device will handle safely.
The formula used for conversion is \( I_A = (G + R) \times I_G \). Here, \( G \) is the galvanometer resistance, \( R \) is the additional resistance, and \( I_G \) the initial current for full scale deflection. Plugging in these values calculates the new current capacity in the converted ammeter.
Understanding resistance calculation ensures that electrical instruments are adapted correctly for higher demands, preventing malfunction and maintaining accuracy.