3 Most FAQ’s of Current Electricity Chapter in Inter 2nd Year Physics (TS/AP)

8 Marks

LAQ-1 : State Kirchhoff’s law for an electrical network. Using these laws deduce the condition for balance in a Wheatstone bridge.

Introduction

Kirchhoff’s Laws are fundamental principles in electrical circuit theory, crucial for analyzing complex electrical networks. These laws consist of Kirchhoff’s Current Law (KCL) and Kirchhoff’s Voltage Law (KVL).

Kirchhoff’s Current Law (KCL)

Kirchhoff’s Current Law states that the total current entering a junction (or node) in an electrical circuit equals the total current leaving the junction. Mathematically, it is expressed as:

$$\sum I_{\text{in}} = \sum I_{\text{out}}$$

This law is based on the principle of conservation of electric charge.

Kirchhoff’s Voltage Law (KVL)

Kirchhoff’s Voltage Law asserts that the sum of the electrical potential differences (voltages) around any closed loop or mesh in a circuit is zero. In formula terms, it is:

$$\sum V = 0$$

This law is derived from the conservation of energy principle.

Deriving the Condition for Balance in a Wheatstone Bridge

A Wheatstone Bridge is a circuit used to measure unknown electrical resistances by balancing two legs of a bridge circuit.

1. Configuration: The Wheatstone Bridge consists of four resistors (R_1​, R₂​, R₃​, R₄​) arranged in a diamond shape. A galvanometer is connected between the middle nodes, and a voltage source across the opposite nodes.
2. Balanced Condition: The bridge is in a balanced state when the voltage across the galvanometer is zero. Applying KVL in the loops and KCL at the middle node, we deduce the condition for balance.
3. Application of Kirchhoff’s Laws:
   • From KVL, in the first loop with resistors R₁​ and R₂​, and in the second loop with resistors R₃​ and R₄​, the voltages across these resistors must be the same when the bridge is balanced.
   • Applying KCL at the middle node ensures no current flows through the galvanometer.
4. Balanced Bridge Equation: The condition for a balanced Wheatstone Bridge is given by the ratio of resistances: $$\frac{R_1}{R_2} = \frac{R_3}{R_4}$$ ​​This equation indicates that the ratios of the resistances in one arm of the bridge are equal to the ratios in the other arm.

Summary

Kirchhoff’s Laws are essential for understanding electrical circuits and are particularly useful in analyzing a Wheatstone Bridge. The condition for balance in a Wheatstone Bridge, derived using these laws, is a critical concept in measuring unknown resistances and ensuring precision in electrical measurements.

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LAQ-2 : State the working principle of potentiometer. explain with the help of circuit diagram how the emf of two primary cells are compared by using the potentiometer.

Introduction

The potentiometer is a device used for measuring the electromotive force (emf) of a cell or comparing emfs of different cells, and for measuring internal resistance of a cell. It operates on the principle that the potential drop across any portion of a wire carrying a constant current is directly proportional to the length of that portion.

Working Principle of Potentiometer

The basic working principle of a potentiometer is the uniform potential drop along a resistive wire with a constant current flowing through it. The potential difference across any segment of the wire is directly proportional to the length of the segment, provided the current in the wire remains constant.

Comparing EMF of Two Primary Cells Using Potentiometer

1. Circuit Setup:
   • The potentiometer circuit consists of a long resistive wire AB of uniform cross-section and known length.
   • The wire is connected in series with a battery (not the cells to be measured), a rheostat, and a key.
   • The cells whose emfs are to be compared are connected in turn to the circuit through a two-way key.
2. Measurement Process:
   • For measuring the emf of the first cell, it is connected in series with a high resistance box and a galvanometer.
   • The jockey is slid along the wire AB until the galvanometer shows no deflection, indicating a null point.
   • At this null point, the emf of the cell is equal to the potential drop across the length of the wire from point A to the null point.
3. Repeat for Second Cell:
   • The process is repeated for the second cell. The length where the null point is achieved gives the measure of its emf.
4. Comparison of EMF:
   • The emf of the two cells is directly proportional to the lengths of the wire segments from A to their respective null points.
   • By comparing these lengths, the relative emfs of the two cells can be deduced.

Summary

The potentiometer is a versatile and accurate instrument used for measuring and comparing the emf of cells. Its principle relies on the uniform potential drop across a resistive wire. When comparing the emf of two cells, the lengths of wire segments to the null points provide a direct comparison of their emfs. This method is widely valued for its precision in voltage measurement without drawing current from the cell.

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LAQ-3 : State the working principle of potentiometer explain with the help of circuit diagram how the potentiometer is used to determine the internal resistance of the given primary cell.

Introduction

A potentiometer is an instrument used to measure the electromotive force (emf) and internal resistance of a cell. It works on the principle of a uniform potential drop along a resistor wire with a constant current flowing through it.

Working Principle of Potentiometer

The fundamental principle of a potentiometer is that the potential drop across a section of a wire is directly proportional to the length of the wire, assuming a constant current. This makes it possible to measure voltages more accurately as it does not draw current from the circuit being measured.

Using Potentiometer to Determine Internal Resistance of a Cell

1. Circuit Setup:
   • The potentiometer setup includes a long wire of uniform resistance, connected in series with a stable battery, a rheostat, and a key.
   • The primary cell whose internal resistance is to be determined is connected to this circuit with a two-way key.
2. Measurement Process:
   • Initially, the cell is connected in open circuit mode to the potentiometer, and a null point is determined. At this null point, the potential difference across the wire equals the emf of the cell.
   • The length of the wire from the starting point to the null point gives a measure proportional to the emf of the cell.
3. Determining Internal Resistance:
   • To measure internal resistance, a known resistance (load) is connected in series with the cell.
   • The circuit is then adjusted to find a new null point. The potential difference at this point is equal to the terminal voltage of the cell.
4. Calculations:
   • Using the lengths corresponding to the emf (open circuit) and terminal voltage (with known resistance), along with the known external resistance, the internal resistance of the cell can be calculated.
   • The formula used is based on the relation: V = E − Ir, where V is the terminal voltage, E is the emf, I is the current, and r is the internal resistance.

Summary

The potentiometer is a precise tool for measuring the internal resistance of a cell. By comparing the potential drop across different lengths of wire, both the emf and the terminal voltage of the cell can be accurately determined. From these measurements, the internal resistance of the cell can be calculated, illustrating the effectiveness of the potentiometer in detailed electrical measurements.