Current Electricity: Electric Current and Ohm's Law

• Current electricity involves the flow of electric charge (electric current) through a conductor

Electric Current

• Electric current (I) is defined as the rate of flow of electric charge through a cross-sectional area
• I = ΔQ/Δt, where ΔQ is the amount of charge flowing in time Δt
• SI unit of electric current is Ampere (A), where 1 A = 1 C/s
• Electric current is a scalar quantity, despite having a direction
• Current density (J) is a vector quantity that describes the electric current per unit area
• J = I/A, where A is the cross-sectional area
• Drift velocity (vd) is the average velocity attained by charged particles in a material due to an electric field
• Current (I) = neAvd , where n is the number density of electrons and e is the charge of an electron

Ohm's Law

• Ohm's law states that the potential difference (V) across a conductor is directly proportional to the current (I) flowing through it, provided the physical conditions and temperature remain constant
• V = IR, where R is the resistance of the conductor
• Resistance (R) is the opposition to the flow of electric current
• SI unit of resistance is Ohm (Ω), where 1 Ω = 1 V/A
• Resistance depends on the material, length, and cross-sectional area of the conductor
• R = ρ(l/A), where ρ is the resistivity of the material, l is the length, and A is the cross-sectional area

Resistivity and Conductivity

• Resistivity (ρ) is a measure of a material's ability to resist electric current
• SI unit of resistivity is Ohm-meter (Ω⋅m)
• Conductivity (σ) is the reciprocal of resistivity, representing a material's ability to conduct electric current
• σ = 1/ρ
• SI unit of conductivity is Siemens per meter (S/m) or (Ω⋅m)−1
• Resistivity and conductivity depend on temperature
• ρ(T) = ρ0[1 + α(T − T0)], where ρ(T) is the resistivity at temperature T, ρ0 is the resistivity at reference temperature T0, and α is the temperature coefficient of resistivity

Electrical Energy and Power

• Electrical energy is the energy associated with the movement of electric charge
• Electrical power (P) is the rate at which electrical energy is consumed or generated
• P = VI = I^2R = V^2/R
• SI unit of power is Watt (W), where 1 W = 1 J/s
• Electrical energy consumed is given by E = Pt, where t is the time for which the power is consumed
• Commonly measured in kilowatt-hours (kWh), where 1 kWh = 3.6 × 10^6 J

Combination of Resistors

• Series combination: Resistors are connected end-to-end, so the same current flows through each resistor
• Equivalent resistance (Rs) = R1 + R2 + R3 + ...
• Parallel combination: Resistors are connected such that the potential difference across each resistor is the same
• Reciprocal of equivalent resistance (1/Rp) = 1/R1 + 1/R2 + 1/R3 + ...

Cells, EMF, and Internal Resistance

• An electric cell is a device that maintains a potential difference across its terminals
• Electromotive force (EMF) (ε) is the potential difference across the terminals of a cell when no current is drawn from it
• Internal resistance (r) is the resistance offered by the cell itself to the flow of current
• Terminal voltage (V) = ε − Ir, where I is the current flowing through the circuit

Kirchhoff's Laws

• Kirchhoff's current law (KCL): The algebraic sum of currents entering a junction is equal to the algebraic sum of currents leaving the junction
• Kirchhoff's voltage law (KVL): The algebraic sum of potential differences in a closed loop is zero
• These laws are used to analyze complex circuits

Wheatstone Bridge

• Wheatstone bridge is an electrical circuit used to measure an unknown resistance
• It consists of four resistors (P, Q, R, and S) connected in a bridge configuration
• When the bridge is balanced (no current flows through the galvanometer), P/Q = R/S
• Unknown resistance can be determined if the other three resistances are known

Potentiometer

• A potentiometer is an instrument used to measure potential difference accurately
• It works on the principle that the potential drop across a uniform wire is directly proportional to its length
• Used to compare EMFs of two cells or to measure the internal resistance of a cell
• Potential gradient, k = V/L, where V is the potential difference across the wire of length L

Special Considerations

• Superconductivity is a phenomenon where certain materials exhibit zero electrical resistance below a critical temperature
• Electric heating occurs due to the conversion of electrical energy into heat when current passes through a conductor
• Thermistors are temperature-sensitive resistors used in various applications for temperature measurement and control

Learn about current electricity, including the definition of electric current as the rate of flow of electric charge. Explore Ohm's Law, which states the relationship between potential difference and current in a conductor, emphasizing the conditions for its validity.