Revision: Current Electricity >> Current Electricity Physics Science (English Medium) Class 12 CBSE

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. 

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

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

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

Current is defined as the rate of flow of charge.

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

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.

A conductor is a material in which some charges are free to move from one part of the material to another.

At constant temperature and other physical conditions, the current flowing through a conductor is directly proportional to the potential difference across its ends.

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.

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.

The average velocity acquired by free electrons in a conductor under the influence of an electric field is called the drift velocity.

The average time interval between two successive collisions of a free electron with the ions of the metallic lattice is called the relaxation time and is denoted by τ.

Current density is the current flowing per unit cross-sectional area of the conductor. The source material connects current density with the drift motion of electrons.

Conductivity, denoted by σσ, measures how easily current flows through a material. From the microscopic model, conductivity depends on free electron density and relaxation time.

Mobility is the magnitude of drift velocity per unit electric field.

A device that does not obey Ohm's law and shows a non-linear or direction-dependent V-I relation.

A device that obeys Ohm's law and gives a straight-line V-I graph through the origin.

Resistivity, denoted by ρ, is the intrinsic property of a material that determines how much it resists current flow.

The temperature coefficient of resistivity, denoted by α, measures the fractional change in resistivity per degree change in temperature in the linear range.

• Unit: per degree Celsius or per kelvin.
• For metals, α > 0.
• For semiconductors, α < 0.

The emf of a cell is defined as the work done in carrying a unit positive charge through the complete circuit, including the charge flow inside the cell.

Unit: J/C (or) volt

The resistance offered by the electrolyte of the cell when an electric current flows through it is known as internal resistance.

When current is drawn through a cell or current is supplied to it, then the potential difference across its terminals is called the terminal potential difference.

\[V=E-Ir\]

An instrument used to measure the potential difference between two points in an electrical circuit, always connected in parallel with the component across which the voltage drop is to be measured, is called a voltmeter.

The condition of the Wheatstone bridge under which the galvanometer shows zero (null) deflection, i.e., I_g = 0, is called the balance condition of the bridge.

An arrangement of four resistors used to measure the resistance of one of them in terms of the other three, invented by Samuel Hunter Christie in 1833 and made famous by Sir Charles Wheatstone, is called a Wheatstone bridge.

I = \[\frac {Q}{t}\]

Where:

• I = electric current
• Q = charge flowing through the conductor
• t = time taken

SI unit of current = ampere (A).

V ∝ I

V = IR

Other useful forms: I = \[\frac {V}{R}\] or R = \[\frac {V}{I}\]

Using the average time between collisions ττ, the source derives the drift velocity as: 

μ = \[\frac {∣v_d​∣}{E}\]​

where:

ρ_T ​= ρ₀​[1 + α(T − T₀​)]

Here:

• ρ_T​ = resistivity at temperature T.
• ρ₀​ = resistivity at reference temperature T₀.
• α = temperature coefficient of resistivity.

R_T ​= R₀​(1 + αΔT)

where ΔT = T − T₀​.

Balance condition (when I_g = 0):

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.

Statement

At any junction in an electric circuit, the sum of currents entering the junction is equal to the sum of currents leaving the junction. 

Derivation

When the current in a circuit is steady, charge does not accumulate at any junction. Therefore, the amount of charge entering the junction per second must be equal to the amount of charge leaving the junction per second. 

If currents I₁​ and I₂ enter a junction and currents I₃​ and I₄​ leave it, then

or

Hence,

Conclusion

Kirchhoff's First Law is a direct consequence of the conservation of charge. 

Statement

In any closed loop of an electric circuit, the algebraic sum of all changes in potential is zero. 

Derivation

Consider a charge moving around a closed loop. After completing one full loop, the charge returns to its starting point. Since electric potential depends only on position, the net change in potential over a complete loop must be zero. 

Therefore, in a closed loop,

If a loop contains cells and resistors, then the total emf supplied by the sources is equal to the total potential drop across the resistors. Thus,

Conclusion

Kirchhoff's Second Law is a direct consequence of the conservation of energy.

The algebraic sum of potential differences in a closed loop is zero.

Based on conservation of energy.

At any junction, the sum of currents entering = the sum of currents leaving.

Example: I₁ + I₃ = I₂ + I₄​. Based on conservation of charge.

Let `I_3` and `I_4`  be the currents in resistors Q and S respectively . Let `I_g` be the current through galvanometer. For balanced condition, 

`I_g = 0`

Applying junction law at ‘b’ we get

`I_1 = I_3 + I_g`

`because I_g = 0 , I_1 = I_3`    ....(i)

Applying junction law at ‘d’, we get

`I_2 + I_g = I_4`

`because I_g = 0 , I_2 = I_4`    ....(ii)

Applying loop law in the loop abda, we get

`-I_1·P - I_g·Q + -I_2·R = 0`

⇒ `-I_1P + I_2R = 0`  (`because I_g = 0`)

⇒ `I_1P = I_2R`

⇒ `P/R = I_2/I_1`               ....(iii)

Applying loop law in the loop bcdb, we get

`-I_3·Q + I_4·S + I_g·6 = 0`

⇒ `-I_3·Q + I_4·S + 0 = 0  (because I_g =0)`

⇒ `-I_3Q = I_4S`

⇒ `Q/S = I_4/I_3`

⇒ `Q/S = I_2/I_1`             ...(iv) [using eq.(i) and (ii)]

From eq. (iii) and (iv), `P/ R = Q/s`

⇒ `P/Q = R/S`

This is the balanced condition. 

• 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.

Resistivity and Temperature:

\[\rho_T=\rho_0[1+\alpha(T-T_0)]\]

Resistance and Temperature:

\[R_T=R_0(1+\alpha\Delta T)\]

Temperature Coefficient (α):

• Unit: °C⁻¹ (or K⁻¹)
• Metals: α > 0→ resistivity increases with temperature

Semiconductors & insulators:

α < 0 → resistivity decreases with temperature

• In series: ε_eq​ adds, r_eq adds. 

• If one cell is reversed in series, the net emf is the difference of emfs, but internal resistances still add. 

• In parallel, effective internal resistance decreases. 

• For two cells in parallel:
  ε_eq = \[\frac{\varepsilon_1r_2+\varepsilon_2r_1}{r_1+r_2}\], r_eq = \[\frac{r_1r_2}{r_1+r_2}\]​​. 

• Kirchhoff's laws are used for complex circuits. 
• Kirchhoff's First Law: Total current entering a junction = total current leaving a junction. 
• Kirchhoff's Second Law: Total potential rise in a closed loop = total potential drop in the loop. 
• KCL is based on conservation of charge. 
• KVL is based on conservation of energy. 
• Mathematical forms are ∑I = 0 and ∑V = 0. 
• The correct sign convention is essential in numericals.