Electric charge and current
Section: Electricity | Syllabus: Cambridge AS Level Physics 9702
Electric Current Electric current is defined as the rate of flow of electric charge past a point in a circuit. Electric Current The rate of flow of charge: I = fraction or equivalently Q = It Current is measured in amperes (A) .
One ampere is the current when one coulomb of charge passes a point in one second. SI Definition The ampere is defined based on the fixed value of the elementary charge e = 1.602\,176\,634 × 10^-19 C.
Key Equation Charge-Current Relationship Q = It where Q = charge (C), I = current (A), t = time (s) Charge Carriers in Different Media Electric current requires charge carriers - particles that are free to move and carry electric charge.
The type of charge carrier depends on the medium: Medium Charge Carriers Notes Metals Free (delocalised) electrons Electrons move freely between fixed positive metal ions Electrolytes Positive and negative ions Both types of ion contribute to current in opposite directions Semiconductors Electrons and holes Fewer charge carriers than metals; number increases with temperature Ionised gases / Vacuum Electrons and ions Free electrons can also travel through vacuum (e.g., cathode ray tubes) FIG 9.1: Conduction Electrons in a Metal Show positive metal ions arranged in a regular lattice structure with free (delocalised) electrons represented as smaller particles moving randomly in the spaces between the ions.
FIG 9.2: Movement of Ions in an Electrolyte Show a beaker containing an electrolyte solution with two electrodes connected to a battery. Positive ions (cations) move towards the cathode (negative electrode) and negative ions (anions) move towards the anode (positive electrode).
Quantisation of Charge Electric charge is quantised , meaning it exists only in discrete amounts. The smallest unit of charge is the elementary charge , e. Elementary Charge e = 1.60 × 10^-19 C All observable charges are integer multiples of e: Charge on an electron: -e = -1.60 × 10^-19 C Charge on a proton: +e = +1.60 × 10^-19 C Calculating Number of Electrons The number of electrons in a given charge is found by: Number of Electrons n = fraction where n = number of electrons, Q = total charge (C), e = 1.60 × 10^-19 C Worked Example: Charge and Electron Count Question: A current of 0.75 A flows through a lamp for 15 minutes.
Calculate (a) the charge that flows, and (b) the number of electrons that pass through the lamp. Solution (a) Calculate charge: Q = It = 0.75 × (15 × 60) = 0.75 × 900 Q = 675 C (b) Calculate number of electrons: n = fraction = fraction n = 4.22 × 10^21 electrons Conventional Current vs Electron Flow Conventional current is defined as flowing from the positive terminal to the negative terminal of a power supply.
However, in metallic conductors, the actual charge carriers (electrons) flow in the opposite direction - from negative to positive. FIG 9.3: Conventional Current vs Electron Flow Show a simple circuit with a battery and wire.
Include arrows indicating conventional current direction (from + to −) and separate arrows showing electron flow direction (from − to +) in the opposite direction. Historical Note The direction of conventional current was defined before electrons were discovered (1897).
We continue to use this convention today. Drift Velocity In a metal, free electrons move randomly at high thermal speeds (typically 10^6 m s^-1). When a potential difference is applied, electrons also drift slowly towards the positive terminal.
FIG 9.4: Electron Drift in a Metal Wire Show a conduction electron's path as it moves through a wire, colliding with metal ions. Illustrate the fast random thermal motion (zig-zag path) combined with a slow net drift towards the positive terminal of the connected battery.
Mean Drift Velocity The average velocity of charge carriers in the direction of current flow, typically very small (mm s^-1 in metals). The Current Equation Consider a conductor of cross-sectional area A carrying current I.
If the charge carriers have: number density n (number of charge carriers per unit volume, in m^-3) charge q on each carrier (in C) mean drift velocity v (in m s^-1) Current Equation I = Anvq where I = current (A), A = cross-sectional area (m^2), n = number density (m^-3), v = drift velocity (m s^-1), q = charge per carrier (C) Derivation of I = Anvq FIG 9.5: Wire Section for Deriving I = Anvq Show a cylindrical section of wire with length d and cross-sectional area A clearly labelled.
Include the positive terminal of the battery on one side and show charge carriers (electrons) distributed throughout the volume of the wire. Consider a wire of length d and cross-sectional area A: Volume of wire section: V = A × d Number of charge carriers in this volume: N = n × A × d Total charge in this section: Q = N × q = nAdq If electrons travel distance d in time t: drift velocity v = fraction, so d = vt Substituting: Q = nA(vt)q Current: I = fraction = fraction = Anvq Worked Example: Drift Velocity Calculation Question: A copper wire has cross-s…
Interactive revision notes, videos and practice questions load below.