Problem 172 - A Complete Resource Book in Physics for JEE Main

Question

This question has statement I and statement II. Of the four choices given after the statements, choose the one that best describes the two statements. Statement-I: Higher the range, greater is the resistance of ammeter. Statement-II: To increase the range of ammeter, additional shunt needs to be used across it. (A) Statement-I is true, Statement-II is true, Statement-II is not the correct explanation of Statement-I. (B) Statement-I is true, Statement-II is false. (C) Statement-I is false, Statement-II is true. (D) Statement-I is true, Statement-II is true, Statement-II is correct explanation of Statement-I.

Step-by-Step Solution

Answer

(C) Statement-I is false, Statement-II is true.

Step 1: Understanding ammeter and its range

An ammeter is a device used to measure electric current in a circuit. The range of an ammeter refers to the maximum amount of current it can measure accurately without any damage to the device.

Step 2: Understanding the resistance of an ammeter

Resistance is the opposition to the flow of electric current in a circuit, measured in ohms. The resistance of the ammeter should ideally be as low as possible so that it doesn't affect the current flow in the circuit when connected.

Step 3: Understanding the role of shunt in an ammeter

A shunt is a low-resistance device connected in parallel with the ammeter to increase its range. The shunt allows the majority of the current to pass through it while allowing only a small portion to flow through the ammeter. The ratio of the current passing through the ammeter to the total current in the circuit will remain constant, which enables the ammeter to accurately measure a larger current.

Step 4: Statement I Analysis

The statement, "Higher the range, greater is the resistance of ammeter", is FALSE. Because, to increase the range, an ammeter should have a lower internal resistance, not a greater resistance.

Step 5: Statement II Analysis

The statement, "To increase the range of ammeter, additional shunt needs to be used across it", is TRUE. As explained in step 3, adding a shunt in parallel to the ammeter will allow a larger current to be measured accurately. Based on the above analysis, the correct option will be: (C) Statement-I is false, Statement-II is true.

Key Concepts

Electric Current Measurement

Understanding electric current measurement is crucial in circuits. An ammeter is a special device designed for this purpose. It measures the flow of electric charge through a conductor per unit time, which is the electric current. The unit of electric current is the ampere, symbolized as A. For precise measurement, the ammeter must be connected in series with the part of the circuit where current needs to be measured.

There are different types of ammeters, including digital and analog versions. Digital ammeters extract data and display it in numerical form, often resulting in more precise readings. Analog ammeters, on the other hand, use a needle to indicate the current on a scaled dial, which can be interpreted by the user.

• Formula for current: \( I = \frac{Q}{t} \,\) where \( I \,\) is the current, \( Q \,\) is the charge, and \( t \,\) is the time.
• Typical applications: monitoring battery charge, electric circuit analysis, and electrical engineering projects.

Resistance in Circuits

Resistance is a crucial factor in electrical circuits, as it opposes the flow of electric current. It is measured in ohms, represented as \( \Omega \,\). A fundamental property of wires and components, resistance affects how easily electric charges can move through them.

Conductors and insulators show different resistance characteristics. Conductors have low resistance and permit easy flow of electric current. Common conductors include metals like copper and aluminum. Insulators, such as rubber and glass, have high resistance and inhibit current flow.

• Ohm's Law: \( V = IR \,\) where \( V \,\) is voltage, \( I \,\) is current, and \( R \,\) is resistance.
• Factors affecting resistance include material, length, cross-sectional area, and temperature of the conductor.

Understanding resistance is essential for designing circuits, as it impacts both performance and efficiency.

Role of Shunt in Ammeter

The role of the shunt in an ammeter is to extend the range of current measurement. This is achieved by placing a low-resistance component, known as a shunt, parallel to the ammeter. When a current is measured, most of it flows through the shunt due to its lower resistance.

This design ensures that only a small fraction of the current flows through the ammeter itself. The current in the ammeter remains within its safe operational limits while still allowing the electrons to flow through the circuit without much resistance.

• Shunt Formula: \( I_s = \frac{V}{R_s} \,\), where \( I_s \,\) is the current through the shunt, \( V \,\) is the voltage, and \( R_s \,\) is the resistance of the shunt.
• Accuracy: The ammeter can still accurately reflect the total circuit current based on the calibration with the shunt.

Adding a shunt makes it possible to measure larger currents with a relatively small deflection in ammeter readings, enhancing its functionality without compromising safety.