Introduction
Current electricity refers to the flow of electric charges in a conductor. In this chapter, we will cover the concept of electric current, Ohm’s law, resistance, resistivity, combination of resistors,
1. Electric Current:
- Definition: Electric current is the flow of electric charge through a conductor. It is the rate at which charge flows.
- Formula: Electric current I is given by the formula:
( I = \frac{Q}{t} )
Where,
( I ) = Electric current (measured in amperes)
( Q ) = Charge (measured in coulombs)
( t ) = Time (measured in seconds) - Unit: The SI unit of electric current is the ampere (A).
- Direction of Current: By convention, the direction of current is taken as the direction in which positive charges flow. In metallic conductors, current is due to the flow of electrons, which move in the opposite direction to the conventional current.
2. Ohm’s Law:
- Statement: Ohm’s Law states that the current flowing through a conductor is directly proportional to the potential difference across its ends, provided the temperature remains constant.
- Formula:
( V = IR )
Where,
( V ) = Potential difference (volts)
( I ) = Current (amperes)
( R ) = Resistance (ohms)
3. Resistance:
- Definition: Resistance is the property of a conductor to resist the flow of current through it.
- Formula:
( R = \frac{V}{I} )
Where,
( R ) = Resistance
( V ) = Potential difference
( I ) = Current - Unit: The SI unit of resistance is ohm, represented by the Greek letter omega.
- Factors Affecting Resistance:
- Length of the conductor: Resistance is directly proportional to the length of the conductor.
- Cross-sectional area: Resistance is inversely proportional to the cross-sectional area of the conductor.
- Nature of the material: Different materials have different resistivities, which affect their resistance.
- Temperature: For most materials, resistance increases with an increase in temperature.
4. Resistivity:
- Definition: Resistivity is the intrinsic property of a material that indicates how much it resists the flow of electric current.
- Formula:
( R = \rho \frac{L}{A} )
Where,
( R ) = Resistance
( \rho ) = Resistivity of the material
( L ) = Length of the conductor
( A ) = Cross-sectional area - Unit: The SI unit of resistivity is ohm meter.
5. Combination of Resistors:
Resistors can be combined in two ways:
a) Series Combination:
- In series, the resistors are connected end to end.
- The current is the same through all resistors, but the potential difference is divided.
- Formula for total resistance:
( R_{total} = R_1 + R_2 + R_3 + … )
b) Parallel Combination:
- In parallel, the resistors are connected across the same two points.
- The potential difference is the same across all resistors, but the current is divided.
- Formula for total resistance:
( \frac{1}{R_{total}} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3} + … )
6. Electromotive Force (EMF) and Potential Difference:
- EMF: EMF is the energy supplied by a source (such as a battery) to drive a unit charge around a complete circuit.
- Potential Difference: It is the work done in moving a unit charge between two points in a circuit.
- Difference between EMF and Potential Difference:
- EMF is the total energy per unit charge provided by a source.
- Potential difference is the energy used per unit charge between two points in a circuit.
7. Kirchhoff’s Laws:
a) Kirchhoff’s First Law (Junction Rule):
- It states that the sum of currents entering a junction is equal to the sum of currents leaving the junction.
b) Kirchhoff’s Second Law (Loop Rule):
- It states that the sum of the potential differences around any closed loop in a circuit is zero.
8. Wheatstone Bridge:
- Definition: A Wheatstone bridge is an arrangement of four resistances in a diamond shape. It is used to measure unknown resistance.
- Condition for Balance: For the bridge to be balanced, the ratio of resistances in one branch must be equal to the ratio of resistances in the other branch.
9. Meter Bridge:
- Definition: A meter bridge is a practical application of the Wheatstone bridge. It consists of a one-meter-long wire with known and unknown resistances connected across it.
- Purpose: It is used to determine the unknown resistance by balancing the bridge.
10. Electric Power:
- Definition: Electric power is the rate at which electrical energy is consumed or produced in a circuit.
- Formula:
( P = VI )
Where,
( P ) = Power (watts)
( V ) = Potential difference (volts)
( I ) = Current (amperes)
11. Heating Effect of Electric Current:
- Joule’s Law of Heating: The heat produced in a conductor due to the flow of current is proportional to the square of the current, the resistance, and the time for which the current flows.
- Formula:
( H = I^2 R t )
Where,
( H ) = Heat energy (joules)
( I ) = Current (amperes)
( R ) = Resistance (ohms)
( t ) = Time (seconds)
12. Applications of Heating Effect:
- Electric heating appliances like electric irons, heaters, toasters, etc., use the heating effect of electric current.
- Electric bulbs convert electric energy into light and heat energy using this principle.
