Current Electricity

The One Thing

Current electricity concerns the ordered motion of charge caused by a potential difference. Circuit behaviour is determined by the relationship between potential difference, resistance, current, and the characteristics of real cells, including their internal resistance.

Reactions, Processes and Experiments

Key Terms

• Electric current: The rate of flow of electric charge through a cross-section, given by I = Q/t; its SI unit is the ampere.
• Conventional current: The direction in which positive charge would move, from higher potential to lower potential in an external circuit.
• Drift velocity: The small average velocity acquired by free electrons in a conductor because of an applied electric field.
• Current density: Current flowing per unit area perpendicular to the flow, given by J = I/A.
• Potential difference: The work done per unit charge in moving a test charge between two points, V = W/Q.
• Ohm’s law: For a conductor at constant temperature and physical conditions, current is directly proportional to potential difference: V = IR.
• Resistance: The opposition offered by a conductor to the flow of current; R = V/I and its SI unit is the ohm.
• Resistivity: A material property defined by rho = RA/l, where R is resistance, A is cross-sectional area, and l is length.
• Conductivity: The reciprocal of resistivity, sigma = 1/rho, indicating how easily a material conducts electricity.
• Temperature dependence of resistance: For many metals over a limited range, R_T = R_0[1 + alpha(T - T_0)], where alpha is the temperature coefficient of resistance.
• EMF: The energy supplied by a source per unit charge when no current is drawn; it is denoted by E and measured in volts.
• Internal resistance: The resistance inside a cell or battery that causes energy loss when current flows; it is denoted by r.
• Terminal potential difference: The voltage available across the terminals of a cell while supplying current; for a discharging cell, V = E - Ir.
• Kirchhoff’s junction rule: The algebraic sum of currents at a junction is zero; total current entering a junction equals total current leaving it.
• Kirchhoff’s loop rule: The algebraic sum of potential changes around any closed loop is zero, expressing conservation of energy.
• Resistors in series: The same current flows through each resistor and the equivalent resistance is R_s = R_1 + R_2 + ... .
• Resistors in parallel: The same potential difference acts across each branch and 1/R_p = 1/R_1 + 1/R_2 + ... .
• Electrical power: The rate of electrical energy consumption, P = VI = I^2R = V^2/R.
• Electrical energy: Energy used in time t, W = VIt = I^2Rt; the commercial unit is the kilowatt-hour.
• Wheatstone bridge: A bridge circuit used to measure an unknown resistance; at balance, P/Q = R/S and no current flows through the galvanometer.
• Meter bridge: A practical form of the Wheatstone bridge using a uniform wire; at balance, X/R = l/(100 - l), subject to the chosen arm arrangement.
• Potentiometer: An instrument that measures potential difference by comparing it with the potential drop along a uniform resistance wire.
• Potential gradient: Potential drop per unit length of potentiometer wire, k = V/L.
• Null point: The position on a potentiometer wire where the galvanometer shows zero deflection, indicating no current through it.

Easily Confused

• EMF and terminal potential difference: EMF is the energy supplied per unit charge when no current is drawn, whereas terminal potential difference is the voltage available while the cell supplies current; for a discharging cell, V = E - Ir.
• Electron drift and conventional current: Electrons drift opposite to conventional current, which is defined as the direction of positive charge motion.
• Resistance and resistivity: Resistance depends on a conductor’s material and dimensions, whereas resistivity is a material property defined by rho = RA/l.
• Series and parallel resistors: In series, the same current flows through every resistor; in parallel, the same potential difference acts across every branch.
• Kirchhoff’s junction rule and loop rule: The junction rule follows conservation of charge, whereas the loop rule follows conservation of energy.
• Wheatstone bridge and meter bridge: The meter bridge is a practical Wheatstone bridge using a uniform wire and a balance length.
• Potentiometer and voltmeter: A potentiometer uses a null point and draws no current from the source being measured at balance, making it more accurate for comparing emfs.
• Power supplied by a cell and useful external power: P = EI is the power supplied by the cell, whereas P_external = VI = I^2R is the useful power delivered to the external resistance.
• Potential gradient and sensitivity: A smaller potential gradient gives a greater potentiometer sensitivity; therefore, a longer wire generally increases sensitivity.

What Gets Asked

• Define electric current, potential difference, resistance, resistivity, conductivity, emf, internal resistance, and terminal potential difference, including their equations and SI units. A common mark-losing error is confusing emf with terminal potential difference under load.
• Derive or apply microscopic current relations, especially I = neAv_d and J = ne v_d. The direction of electron drift must not be identified with the direction of conventional current.
• Calculate equivalent resistance for series and parallel combinations, including R_p = R_1R_2/(R_1 + R_2) for two parallel resistors. The key distinction is same current in series and same potential difference in parallel.
• Solve cell and circuit problems using I = E/(R + r), V = E - Ir, V = E + Ir, and the maximum-power condition R = r. Marks are lost when internal resistance is omitted or when charging and discharging equations are interchanged.
• Apply Kirchhoff’s junction and loop rules to complex circuits. The junction rule expresses conservation of charge, while the loop rule expresses conservation of energy.
• Determine unknown resistance or emf using Wheatstone bridges, meter bridges, and potentiometers. The balance condition must be matched to the stated arm arrangement, and the null point must be interpreted as zero galvanometer deflection.