Revision: The Electric Spark Science and Technology 1 SSC (English Medium) 10th Standard Maharashtra State Board

Electric potential is a measure of work done on the unit's positive charge to bring it to that point against all electrical forces. It is represented as ‘V’.

The potential difference (p.d.) between two points is equal to the work done per unit charge in moving a positive test charge from one point to the other.

OR

The work done per unit positive charge in moving a charge from one point to another in an electric field, is called potential difference between those two points.

The potential at a point is defined as the amount of work done per unit charge in bringing a positive test charge from infinity to that point.

 Potential difference: The potential difference between two points may be defined as the work done in moving a unit positive charge from one point to the other.

Current density is a vector quantity, often known as an area vector or cross-sectional area vector, whose value is equal to the electric current flowing per unit area.

J = `"I"/"A"`

S.I unit is A/m².

One coulomb is the amount of electric charge transferred by a current of one ampere in one second.

One ohm is the resistance of a component when the potential difference of one volt applied across the component drives a current of one ampere through it.

The temperature coefficient is defined as the ratio of the increase in resistivity per degree rise in temperature to its resistivity at T₀.

The reciprocal of resistance is called conductllnce. It is denoted by the letter G. 

The solution through which the electricity passes is called an electrolyte.

Electric fuse is a safety device which is used in household wiring and in many appliances.

When a resistor is connected in an electrical circuit, heat is produced in it due to the current. This is known as the heating effect of current.

In an electrical circuit, electric power is defined as the rate at which electrical energy is supplied by the source.

Electric power (P) is the rate at which electrical energy is transferred or consumed in an electrical circuit.

V = \[\frac {W}{Q}\]

or

W = QV

Electric Power P = \[\frac {W}{t}\] = VI = \[\frac {V^2}{R}\] = I²R

According to Ohm’s law, the current flowing in a conductor is directly proportional to the potential difference across its ends, provided the physical conditions and temperature of the conductor remain constant.
No, it is not always true. E.g., Diode valve, junction diode, etc., do not obey Ohm’s law.

Statement: Ohm’s Law

"The electric current flowing through a conductor is directly proportional to the potential difference across its ends, provided the temperature and other physical conditions of the conductor remain constant."

Mathematically,

I ∝ V or V = I R

where:

• V = Potential difference (in volts)
• I = Current (in amperes)
• R = Resistance of the conductor (in ohms, Ω)

Explanation:

When two conductors at different electric potentials are joined by a metallic wire, electrons flow from the conductor at a lower potential (excess electrons) to the one at a higher potential (deficit of electrons). This movement of electrons results in an electric current.

• The current continues to flow until both conductors reach the same potential.
• For continuous current flow, a constant potential difference must be maintained across the ends of the conductor (e.g., using a battery or power supply).

Derivation / Mathematical Proof:

From Ohm’s Law:

I ∝ V ⇒ \[\frac {V}{I}\] = constant

This constant is defined as the resistance (R) of the conductor. Therefore,

V = I R   ---(1)

This is the mathematical form of Ohm’s Law.

Special Case:

If the current I = 1 A, then:

V = R

This implies that the resistance of a conductor is numerically equal to the potential difference across it when 1 ampere of current flows through it.

Conclusion:

Ohm's Law provides a fundamental relationship between voltage, current, and resistance in an electric circuit. It is widely used in the design and analysis of electrical and electronic systems.

• In a parallel combination, the potential difference across each resistor is the same as that across the terminals of the battery.
• The total current in a parallel circuit is equal to the sum of the currents in the individual branches, and the equivalent resistance is less than the smallest resistance connected.

• Electrical power represents the rate at which electrical energy is supplied by the source in an electric circuit.
• The S.I. unit of electrical power is a watt (W), and larger units such as kilowatt, megawatt, and gigawatt are used for measuring higher power.