Problem 133 - A Complete Resource Book in Physics for JEE Main

Question

Column-I (A) During the charging of capacitor (B) Terminal potential of battery is (C) When tre charge flows from higher potential to lower potential through a resistance (D) Work done to carry unit tre charge from negative terminal to positive terminal Column-II 1\. Heat loss will be take place 2\. emf of battery 3\. emf of battery when current through it is zero. 4\. inside the battery electron transfer from -ve terminal of battery to +re terminal of battery.

Step-by-Step Solution

Answer

(A)-2, (B)-3, (C)-1, (D)-4

Step 1: Understand the Components

The first thing to do is to understand key concepts in each statement of Column-I and match them with the given options in Column-II. (A) pertains to the concept of charging a capacitor; (B) is about the terminal potential of a battery; (C) is about the charge flow from high to low potential over a resistance; (D) is about work done to carry unit charge from the negative terminal to the positive terminal of a battery.

Step 2: Match the Statements

We then match each statement in Column-I with the correct concept in Column-II. (A) matches with 2 since charging a capacitor is powered by the battery's electromotive force (emf). (B) matches with 3 since the terminal potential of a battery is effectively its emf when no current flows through it. (C) matches with 1 since when charge flows from a higher potential to a lower potential through a resistance, there is a resulting heat loss due to the energy dissipated. (D) matches with 4 since work is done as electrons are moved from the negative terminal to the positive terminal inside the battery.

Step 3: Verify Your Matches

Once we have matched each statement in Column-I with the correct concept in Column-II, we should check to ensure these matches make sense based on our understanding of electricity and magnetism. If they are consistent with the relevant concepts and principles, then our matches are correct.

Key Concepts

Charging of Capacitor

Charging a capacitor involves the storage of electric energy in an electric field. This happens when a voltage source, such as a battery, is connected to a capacitor. The battery's electromotive force (EMF) starts directing the charge from one plate of the capacitor to the other.

As the charges accumulate on the capacitor plates, an electric field develops between them. The charging process continues until the potential difference across the capacitor matches the EMF of the battery. At this point, the capacitor is fully charged.
Understanding this process is key because it forms the basis for how capacitors work in circuits, where they can release stored energy as needed.

Terminal Potential of Battery

The terminal potential of a battery is the voltage available between its terminals. When no current flows, this potential is equal to the battery's electromotive force (EMF). As the current begins to flow, the terminal potential decreases slightly due to internal resistance within the battery.

This relationship can be expressed as:
\[ V = E - Ir \]

Where:

• \( V \) is the terminal potential
• \( E \) is the EMF
• \( I \) is the current
• \( r \) is the internal resistance

Understanding terminal potential is crucial for analyzing how batteries perform under load and how they power devices in real-world applications. Knowing the terminal potential helps in assessing battery efficiency and capacity.

Current Flow and Resistance

When electrical charge moves from a high potential to a low potential, it often meets resistance, which results in energy being dissipated as heat. This heat loss is a critical factor in how circuits function. Resistance can be thought of as the roadblock that causes energy to convert into heat rather than doing useful work.

Ohm's Law, the foundation for understanding electrical resistance, is expressed as:
\[ V = IR \]
Where:

• \( V \) is the voltage
• \( I \) is the current
• \( R \) is the resistance

Understanding resistance and heat dissipation is essential for designing efficient electrical circuits and improving their performance. It explains why some devices get warm during operation and highlights the importance of materials with low resistance for efficient energy transfer.

Electron Transfer in Battery

Inside a battery, electron transfer is the driving force that creates electric current. Electrons move from the negative terminal (anode) towards the positive terminal (cathode) through an external circuit when connected. This flow of electrons is what powers devices connected to the battery.

Within the battery itself, chemical reactions occur to sustain this electron transfer. These reactions differ between battery types but generally involve the movement of ions through an electrolyte ensuring electron movement can continue.
Understanding this concept is key to comprehending how batteries generate electricity and what contributes to their eventual depletion.