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Science Grade XII Physics

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Chapter 3: Current Electricity

Grade 12 Science | Chapter 3

Current Electricity

Moving charges form an electric current. This chapter develops current and Ohm’s law, resistance and resistivity, combinations of resistors, cells and EMF, and the Wheatstone bridge.

Core Concepts

Key Principles

Worked Examples

Practice Sets

Contents

Introduction: Electric Current

Ohm’s Law

Resistance and Resistivity

Combinations of Resistors

Cells and EMF

The Wheatstone Bridge

Key Reasoning (Principles)

Worked Examples (10)

Practice Sets A to D

10.

Summary and Exam Quick-Check

1. Introduction: Electric Current

An electric current is a flow of charge. It is measured as the charge passing a point each second, I equals q divided by t, in amperes. In a metal wire the current is carried by moving electrons, although by convention current is taken to flow from the positive to the negative terminal. A steady current needs a source, such as a cell, to keep pushing the charge around the circuit.

Core idea

Current is the rate of flow of charge, I equals q divided by t. Ohm’s law links it to voltage and resistance, V equals I times R, and a cell’s EMF drives the current.

2. Ohm’s Law

Ohm’s law states that, for many conductors at constant temperature, the current is proportional to the voltage across them, V equals I times R, where R is the resistance. A conductor that obeys this is called ohmic, and its graph of current against voltage is a straight line through the origin, whose slope is one over the resistance. The steeper the line, the smaller the resistance.

Diagram 1 – A Simple Circuit

A simple circuit with a cell, a resistor and a current

Fig 1. A cell drives a current I through a resistor R; Ohm’s law gives V equals I times R.

3. Resistance and Resistivity

Resistance, measured in ohms, is how strongly a conductor opposes the current. It depends on the material and the shape: resistance is larger for a longer wire and smaller for a thicker one, R equals rho times length divided by area, where rho is the resistivity, a property of the material. For most metals the resistance also rises with temperature.

Diagram 2 – Ohmic Conductor

A straight line graph of current against voltage with slope one over R

Fig 2. For an ohmic conductor the current is proportional to the voltage, a straight line through the origin.

4. Combinations of Resistors

Resistors can be joined in two ways. In series, the same current flows through each and the resistances add, R equals R1 plus R2. In parallel, the same voltage is across each and the reciprocals add, one over R equals one over R1 plus one over R2, so the combined resistance is less than the smallest. These rules let any required resistance be built up from standard values.

5. Cells and EMF

A cell drives current around a circuit. Its electromotive force, or EMF, is the energy it gives each unit of charge, also measured in volts. A real cell has a small internal resistance of its own, so the voltage it delivers to the circuit, the terminal voltage, is a little less than the EMF when a current flows. The lost voltage is used inside the cell itself.

6. The Wheatstone Bridge

The Wheatstone bridge is a clever arrangement of four resistors used to measure an unknown resistance accurately. A galvanometer connects the two midpoints. When the bridge is balanced, no current flows through the galvanometer, and the four resistances satisfy P divided by Q equals R divided by S. Knowing three of them, the fourth is found, which makes the bridge a precise measuring tool.

Diagram 3 – The Wheatstone Bridge

A Wheatstone bridge of four resistors with a galvanometer at balance

Fig 3. With four resistors and a galvanometer, balance occurs when P divided by Q equals R divided by S.

7. Key Reasoning (Principles)

Principle 1: Current is the rate of flow of charge

The current measures how much charge passes a point each second, I equals q divided by t, so a larger flow of charge means a larger current.

Principle 2: Ohm’s law links voltage, current and resistance

For an ohmic conductor V equals I times R, so the current rises in proportion to the voltage and falls as the resistance grows.

Principle 3: Balance means no current through the galvanometer

When a Wheatstone bridge is balanced the two midpoints are at the same potential, so no current flows across and P over Q equals R over S.

8. Worked Examples

Example 1

Q: Define electric current.

▶ Show Solution

The charge passing a point each second, I equals q divided by t.

Answer: Rate of flow of charge.

Example 2

Q: In what unit is current measured?

▶ Show Solution

The ampere.

Answer: The ampere.

Example 3

Q: State Ohm’s law.

▶ Show Solution

V equals I times R for an ohmic conductor at constant temperature.

Answer: V = I R.

Example 4

Q: A 12 volt supply drives current through a 4 ohm resistor. Find the current.

▶ Show Solution

I equals V divided by R equals 12 divided by 4.

So I equals 3 ampere.

Answer: 3 ampere.

Example 5

Q: How does resistance depend on the length of a wire?

▶ Show Solution

Resistance is larger for a longer wire.

Answer: It increases with length.

Example 6

Q: Two 3 ohm resistors are in series. Find the total.

▶ Show Solution

In series R equals R1 plus R2 equals 3 plus 3.

So R equals 6 ohm.

Answer: 6 ohm.

Example 7

Q: Two 6 ohm resistors are in parallel. Find the total.

▶ Show Solution

One over R equals one over 6 plus one over 6 equals one over 3.

So R equals 3 ohm.

Answer: 3 ohm.

Example 8

Q: What is the EMF of a cell?

▶ Show Solution

The energy it gives each unit of charge, in volts.

Answer: Energy per unit charge.

Example 9

Q: When is a Wheatstone bridge balanced?

▶ Show Solution

When no current flows through the galvanometer, with P over Q equals R over S.

Answer: At P/Q = R/S.

Example 10

Q: Why is the terminal voltage less than the EMF when current flows?

▶ Show Solution

Because some voltage is lost across the cell’s internal resistance.

Answer: Due to internal resistance.

9. Practice Sets A to D

Set A – Multiple Choice (Basic)

1. Current is measured in: (a) volt (b) ampere (c) ohm (d) watt

2. Ohm’s law is: (a) V = I/R (b) V = I R (c) V = R/I (d) I = V R

3. Resistance is measured in: (a) ohm (b) volt (c) farad (d) ampere

4. In series, resistances: (a) add (b) reciprocals add (c) cancel (d) halve

5. A balanced Wheatstone bridge has galvanometer current: (a) maximum (b) zero (c) reversed (d) infinite

▶ Reveal Answers

1. (b) ampere.

2. (b) V = I R.

3. (a) ohm.

4. (a) add.

5. (b) zero.

Set B – Short Answer (Understanding)

1. Define current and its unit.

2. State Ohm’s law and name the symbols.

3. How does resistance depend on length and thickness?

4. Give the series and parallel rules for resistors.

5. What is EMF and why is terminal voltage smaller in use?

▶ Reveal Answers

1. The charge passing a point each second, in amperes.

2. V equals I times R; V is voltage, I current, R resistance.

3. Resistance increases with length and decreases with thickness (area).

4. Series: R equals R1 plus R2. Parallel: one over R equals one over R1 plus one over R2.

5. EMF is the energy a cell gives each unit charge; terminal voltage is less because some is lost across internal resistance.

Set C – Application and Reasoning

1. A 9 volt cell drives current through a 3 ohm resistor. Find I.

2. Three 2 ohm resistors are in series. Find the total.

3. Why does a thicker wire have less resistance?

4. Why is no current detected in a balanced bridge?

5. Why does a long extension lead lose more voltage?

▶ Reveal Answers

1. I equals 9 divided by 3 equals 3 ampere.

2. R equals 2 plus 2 plus 2 equals 6 ohm.

3. Because charge has more room to flow, so the opposition to current is smaller.

4. Because the two midpoints are at equal potential, so there is nothing to drive a current across the galvanometer.

5. Because its greater length gives more resistance, so more voltage is lost along it.

Set D – Higher Order (Challenge)

1. Explain why the V to I graph of an ohmic conductor is a straight line through the origin.

2. A 10 ohm and a 15 ohm resistor are in parallel. Find the combined resistance.

3. Explain why adding resistors in parallel lowers the total resistance.

4. Explain how a Wheatstone bridge finds an unknown resistance.

5. Explain why resistance usually rises with temperature in a metal.

▶ Reveal Answers

1. Because V equals I times R with R constant, so I is directly proportional to V, giving a straight line whose slope is one over R.

2. One over R equals one over 10 plus one over 15 equals 3 over 30 plus 2 over 30 equals 5 over 30, so R equals 6 ohm.

3. Because each new path gives the current another route, so more charge flows for the same voltage, meaning less overall resistance.

4. Three known resistors are adjusted until the galvanometer reads zero; then P over Q equals R over S gives the unknown from the others.

5. Because the atoms vibrate more when hotter and obstruct the moving electrons more, raising the resistance.

Chapter Summary

Current

Rate of flow of charge, I equals q divided by t, in amperes.

Ohm’s Law

V equals I times R for an ohmic conductor.

Resistance

R equals rho times length divided by area, in ohms.

Combinations

Series: R adds. Parallel: reciprocals add.

Cell and EMF

EMF is energy per unit charge; internal resistance lowers terminal voltage.

Wheatstone Bridge

Balanced when P over Q equals R over S.

Quantity

Unit

Symbol

Current unit

ampere

–

Ohm’s law

V = I R

–

Resistance unit

ohm

–

8-Point Exam Quick-Check

Current is the rate of flow of charge, I equals q divided by t.

Ohm’s law: V equals I times R (ohmic, constant temperature).

Resistance grows with length, falls with thickness: R equals rho L over A.

Series resistors add; parallel reciprocals add.

A cell’s EMF is energy per unit charge; internal resistance lowers terminal voltage.

An ohmic V to I graph is a straight line through the origin.

Wheatstone bridge balances when P over Q equals R over S.

At balance no current flows through the galvanometer.

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Class 12 Physics Chapter 3: Current Electricity, Complete Notes and Practice

This revision guide follows the current NCERT Class 12 Physics syllabus and develops current electricity, covering electric current and the ampere, Ohm’s law and ohmic conductors, resistance and resistivity, combinations of resistors in series and parallel, cells and electromotive force with internal resistance, and the Wheatstone bridge for measuring resistance, with three diagrams, ten worked examples and graded practice. Visit SchoolRevise.com to revise, practise and excel.