Electric Current and Drift Velocity

• Current electricity involves the flow of electric charge through a conductor.

Electric Current

• Electric current (I) signifies the rate at which electric charge (Q) flows through a conductor.
• I = dQ/dt, where current (I) is in amperes, charge (Q) is in coulombs, and time (t) is in seconds.
• The ampere (A) serves as the SI unit for electric current, equivalent to 1 C/s.
• Although current is a scalar quantity, it is associated with a direction that parallels the flow of positive charge.
• The conventional current flows in the direction of positive charge, which is opposite to the flow of electrons.

Drift Velocity

• Drift velocity (vd) denotes the average velocity of charged particles, such as electrons, influenced by an electric field in a material.
• Electrons move randomly in a conductor but drift slowly when an electric field is applied.
• The relationship between current (I), drift velocity (vd), number density of charge carriers (n), charge of each carrier (e), and cross-sectional area (A) is I = nAvde.

Ohm's Law

• Ohm's Law posits that the voltage (V) across a conductor is directly proportional to the current (I) flowing through it, assuming constant physical conditions and temperature.
• Expressed mathematically, V = IR, where R represents the resistance of the conductor.
• Resistance (R) is the measure of opposition to the flow of electric current.
• The ohm (Ω), equivalent to 1 V/A, is the SI unit for resistance.
• Conductors obeying Ohm's Law are known as Ohmic conductors.
• Non-Ohmic conductors, like semiconductors and diodes, do not adhere to Ohm's Law.

Resistance and Resistivity

• The resistance (R) of a conductor is affected by its length (L), cross-sectional area (A), and the material's resistivity (ρ).
• The relationship among these factors is R = ρL/A.
• Resistivity (ρ) quantifies a material's ability to impede electric current.
• The ohm-meter (Ω⋅m) is the SI unit for resistivity.
• Conductivity (σ), the reciprocal of resistivity (σ = 1/ρ), indicates how well a material conducts electric current.
• Siemens per meter (S/m) is the SI unit for conductivity.

Temperature Dependence of Resistance

• Temperature affects the resistance of most materials.
• Resistance generally increases with temperature in metals, following an approximately linear relationship: R(T) = R0[1 + α(T - T0)], where R(T) is the resistance at temperature T, R0 is the resistance at a reference temperature T0, and α is the temperature coefficient of resistance.
• Semiconductors typically exhibit a decrease in resistance with increasing temperature, showing a negative temperature coefficient.

Electrical Energy and Power

• Electrical energy is that associated with the flow of electric charge.
• Electrical power (P) specifies the rate at which electrical energy converts into other forms of energy.
• Power can be calculated using P = VI = I2R = V2/R, where V is voltage, I is current, and R is resistance.
• The SI unit for power is the watt (W), defined as 1 J/s.

Series and Parallel Resistors

• Resistors in series have a total resistance (Rtotal) equal to the sum of individual resistances: Rtotal = R1 + R2 + R3 + .... The current remains constant through each resistor.
• Resistors in parallel have a reciprocal total resistance (1/Rtotal) equal to the sum of the reciprocals of individual resistances: 1/Rtotal = 1/R1 + 1/R2 + 1/R3 + .... The voltage is the same across each resistor.

Cells, EMF, Internal Resistance

• A cell is a device used to maintain a potential difference to drive current within a circuit
• Electromotive force (EMF, ε) refers to the potential difference across a cell's terminals when there is no current flow.
• Internal resistance (r) exists within the cell, causing a voltage drop when current flows.
• When current (I) flows, the terminal voltage (V) of a cell is V = ε - Ir.

Kirchhoff's Laws

• Kirchhoff's Current Law (Junction Rule) states that the total currents entering a junction in a circuit equals the total currents leaving it.
• Kirchhoff's Voltage Law (Loop Rule) states that the algebraic sum of potential differences in any closed circuit loop is zero.

Electrical Instruments

• An ammeter measures the current in a circuit and must be connected in series; an ideal ammeter possesses zero resistance.
• A voltmeter measures the potential difference (voltage) between two points in a circuit and is connected in parallel; an ideal voltmeter has infinite resistance.
• A galvanometer is a sensitive device for detecting and measuring small currents and can be converted into an ammeter or voltmeter using shunt or series resistances.
• A Wheatstone Bridge comprises four resistors used to measure an unknown resistance; the bridge is balanced when the ratio of resistances in one arm equals the ratio in the adjacent arm.
• A potentiometer measures potential difference accurately without drawing current and can compare EMFs of cells and measure a cell's internal resistance.