Revision: Electricity and Magnetism >> Current Electricity Physics (English Medium) ICSE Class 10 CISCE

Electric charge is an intrinsic property of certain fundamental particles (like electrons and protons) that gives rise to electric and magnetic forces, causing them to experience a force when placed in an electromagnetic field.

OR

Electric charge is the physical property of matter that causes it to experience a force when placed in an electric field.

Key facts:

• SI Unit: Coulomb (C)
• Dimensional Formula: [A T] (Ampere × Time)
• Two types exist: positive and negative

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

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.

Current is defined as the rate of flow of charge.

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

 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.

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.

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 the potential difference between those two points.

OR

The potential difference between any two points in the circuit is the amount of energy needed to move one unit of electric charge from one point to the other.

Resistance is the obstacle that the wire presents to the current flow.

A variable resistor has a resistance that can be varied. It is used to vary the amount of current flowing in a circuit.

A fixed resistor has a resistance of a fixed value. Common types of fixed resistors include carbon film resistors and wire-wound resistors.

Conductance is the reciprocal of resistance — a measure of how easily current flows through a conductor.

G = \[\frac {1}{R}\]

Electric resistance is the property of a conductor by virtue of which it opposes the flow of electric current through it.

R = \[\frac {V}{I}\]

Resistivity is a material-dependent property that measures how strongly a material opposes current flow, independent of its shape or size.

ρ = \[\frac {RA}{l}\]

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

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.

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

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.

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

The conductors which do not obey Ohm's law are called non-ohmic resistors (or non-linear resistances).

i.e., Current depends on voltage, but it does not vary linearly.

The conductors which obey Ohm's law are called ohmic resistors (or linear resistances).

i.e., Voltage and current vary linearly in ohmic conductors/materials.

Electrical Resistivity (ρ) is defined as the resistance offered by a conductor of unit length and unit cross-sectional area at a given temperature. It is a characteristic property of the material, independent of its dimensions.

A superconductor is a substance of zero resistance (or infinite conductance) at a very low temperature.

Electromotive Force (emf) is the work done by a cell (or any energy source) in driving a unit positive charge around the complete circuit, including through the cell itself.

The terminal voltage of a cell is defined as the work done per unit charge in carrying a positive test charge around the external circuit connected across the terminals of the cell.

When current is drawn from a cell i.e., when the cell is in closed circuit, the potential difference between the electrodes of the cell is known as its terminal voltage.

The internal resistance (r) of a cell is the resistance offered by the electrolyte and electrodes inside the cell to the flow of ionic current through it.

• SI Unit: ohm (Ω)
• Symbol: r
• Represented in circuits as a resistance in series with the ideal e.m.f. source.

The electrical energy consumed in a circuit is defined as the total work done in maintaining the current in the electric circuit for a given time.

Electrical Energy = \[VIt=I^2Rt=\frac{V^2t}{R}\]

S.I. unit of electric energy is joule (1 kWh = \[3.6\times10^6\mathrm{~J}\])

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

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

The unit in which the consumer pays the cost of electrical energy consumed is kWh.

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

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

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.

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

Where:

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

SI unit of current = ampere (A).

\[V_A-V_B=\frac{W}{Q}\]

V ∝ I

V = IR

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

ε = \[\frac {dW}{dq}\]

SI Unit: volt (V), where 1 V = 1 J C⁻¹
Dimensional Formula: [ML²T⁻³A⁻¹]

Voltage drop in the Cell v = \[\frac {w}{q}\]

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

R = \[\frac {V^2}{P}\]

or

R = \[(\text{voltage rating on the appliance})^2 \over \text{power rating on the appliance}\]

Cost of electricity = electrical energy in kWh × cost per kWh

Energy (in kWh) = power (in kW) × time (in h)

= \[\frac{\text{power (in watt)}\times\text{time (in hour)}}{1000}\]

= \[\frac{V(\mathrm{volt})\times I(\mathrm{ampere})\times t(\mathrm{hour})}{1000}\]

The mathematical expression of Joule’s Law of heating is: H = I² Rt

Where,

H = Produced Heat 
I = Current flowing through the device
t = Time taken
r = Resistance of the appliance

According to Ohm’s law, at a constant temperature, the steady current ‘I’ flowing through a conductor is directly proportional to the potential difference ‘V’ between the two ends of the conductor.

I ∝ V

V = IR

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.

• 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

• Electrical energy supplied by a source equals the work done in moving a charge through a potential difference and is given by W = QV = VIt.
• Using Ohm’s law, electrical energy can also be expressed as W = I²Rt or W = (V²/R) t, and its S.I. unit is joule (J).

• 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.

• Watt-hour (Wh) and kilowatt-hour (kWh) are the commercial units of electrical energy, used instead of joule for practical purposes.
• Electrical energy consumed by household and industrial appliances is measured in kilowatt-hours (kWh) and used to calculate electricity costs.
• One kilowatt-hour represents a large amount of energy, equivalent to the energy used by a high-power appliance in one hour.