Revision: Current Electricity Science SSC (English Medium) 9th Standard Maharashtra State Board

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.

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.

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’.

 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.

An electric current is measured by the amount of electric charge moving per unit time at any point in the circuit.

The magnitude of an electric current is the number of electric charges flowing through a conductor in one second.

Electromotive force: When no current is drawn from a cell, when the cell is in open circuit, the potential difference between the terminals of the cell is called its electromotive force (or e.m.f.).

The movement of the positive charge is called conventional current.

The unit of electric current is ampere (A). When one coulomb charge flows through an electric circuit in one second, then the electric current flowing through the circuit is said to be an ampere. 

The resistivity of a material is the resistance of a wire of that material of unit length and unit area of cross-section.

 Semiconductors: Substances whose resistance decreases with the increase in temperature are named as semiconductors. E.g. manganin, constantan etc.

Substances whose resistance decreases tremendously with decreasing temperature and reaches nearly zero near absolute zero are called superconductors; e.g., lead, tin, etc.

A continuous and closed path of an electric current is called an electric circuit.

Current is defined as the rate of flow of charge.

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 material with electrical conductivity between that of a conductor and an insulator, whose number of charge carriers can be controlled as per requirement, is called a semiconductor. (e.g. Silicon, Germanium)

The different energy levels with continuous energy variation are called energy bands.

The range of energies possessed by valence electrons is called valence band.

The range of energies possessed by conduction electrons is called conduction band.

The energy difference between the valence band and the conduction band is called forbidden energy gap.

The solids which have a large number of free electrons are called conductors. (e.g. Iron, Aluminium)

The solids which have very small number of free electrons are called insulators. (e.g. Glass, Wood)

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

or

W = QV

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.

• Electricity is a convenient and controllable form of energy widely used in homes, industries, schools, and hospitals.
• Electric current is produced when electric charges flow through a conductor, and it flows only through a closed, continuous electric circuit.
• A switch completes or breaks the circuit; when the circuit is broken, current stops flowing, and devices like bulbs do not glow.
• Electric current is the rate of flow of charge, given by the relation I = Q / t, where Q is charge and t is time.
• In metallic wires, electrons are the charge carriers, but by convention, current flows from the positive to the negative terminal, in the opposite direction to electron flow.

• Conductors → E_g = 0 - bands overlap, electrons flow freely.
• Semiconductors → E_g < 3 eV — small gap, conducts at room temperature.
• Insulators → E_g > 5 eV — large gap, no conduction.
• Ge = 0.72 eV, Si = 1.1 eV — both semiconductors.
• Metal conductivity decreases with temp. Semiconductor conductivity increases with temp. 

• In series, resistors are connected one after another (in a single path).
• Current is the same through all resistors.

Equivalent resistance:
R_eq = R₁ + R₂ + R₃ + ...

For n identical resistors:
R_eq = nR

Voltage relation:
V = V₁ + V₂ + V₃

Voltage divider rule:
V₁ : V₂ : V₃ = R₁ : R₂ : R₃

R_eq > R_max

• In parallel, resistors are connected across the same two points (multiple paths).
• Voltage is the same across all resistors.

Equivalent resistance:
\[\frac{1}{R_{eq}}=\frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_3}+\cdots\]

For n identical resistors:
Req = R/n

Current relation:
I = I₁ + I₂ + I₃

Current divider rule:
I₁ : I₂ : I₃ = \[\frac{1}{R_{1}}:\frac{1}{R_{2}}:\frac{1}{R_{3}}\]

R_eq < R_min