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Electric Current Through Conductors

Ch. 11Std 11

Easy Overview

Flip a switch, and light floods the room. Press a button, and a message reaches the other side of the world. But what is actually happening inside those wires? Electric current is the flow of charge - typically electrons moving through conductors. This chapter covers how current flows, what resists it, how circuits behave, and how we measure electrical quantities. You will learn Ohm's law (the relationship between voltage, current, and resistance), Kirchhoff's laws (the rules for analyzing complex circuits), how resistors combine in series and parallel, the Wheatstone bridge and meter bridge for measuring unknown resistance, the heating effect of current (how electric heaters work), and the temperature dependence of resistance. These are the fundamentals of electrical engineering - the physics behind every electronic device you have ever used.

Electric Current and Drift Velocity

Electric current I is the rate of flow of charge: I = dQ/dt. Unit: ampere (A). 1 A = 1 C/s. In metals, current is due to electron flow. Electrons move randomly at high speeds (~10^6 m/s), but when an electric field is applied, they drift slowly (~10^-4 m/s) toward the positive terminal. This drift velocity v_d = I/(neA), where n is number density of electrons, e is charge, A is cross-section area. Current density J = I/A = n e v_d. The direction of conventional current is opposite to electron flow - a historical convention that we are stuck with. Current can be DC (direct current, steady one way) or AC (alternating current, reverses periodically).

Ohm's Law and Resistance

Ohm's law: the potential difference across a conductor is proportional to the current through it, provided temperature and other physical conditions remain constant: V = IR. R is resistance (unit: ohm, O). 1 O = 1 V/A. Resistance depends on the material, length, and cross-section: R = rho L/A, where rho is resistivity (unit: O-m). Conductivity sigma = 1/rho. Conductors have low rho (copper: 1.7 x 10^-8 O-m). Insulators have very high rho (rubber: ~10^13 O-m). Semiconductors have intermediate rho. Not all materials obey Ohm's law - diodes and transistors are non-ohmic. For ohmic materials, the V-I graph is a straight line through the origin.

Temperature Dependence of Resistance

Resistance usually increases with temperature for metals. As metals heat up, atoms vibrate more, making it harder for electrons to flow. For most metals: R_T = R_0 (1 + alpha T), where alpha is the temperature coefficient of resistance (per degree C). For copper, alpha - 0.004 /C - resistance increases by 0.4% per degree C. This is why your phone charger cable gets warm when fast charging - current causes heating, which increases resistance, causing more heating. For semiconductors, resistance decreases with temperature - more heat frees up more charge carriers. This opposite behavior is used in thermistors (temperature sensors). Some alloys like constantan have very low alpha - their resistance stays nearly constant with temperature (used in standard resistors).

Resistors in Series and Parallel

Series: R_eq = R_1 + R_2 + R_3 + ... Same current through each resistor, voltage divides. Equivalent resistance is larger than the largest individual. Parallel: 1/R_eq = 1/R_1 + 1/R_2 + 1/R_3 + ... Same voltage across each, current divides. Equivalent resistance is smaller than the smallest individual. For two resistors in parallel: R_eq = (R_1 R_2)/(R_1 + R_2). This is why adding more bulbs in parallel does not reduce brightness (each gets full voltage), but adding in series makes them dimmer (voltage is shared). In household wiring, appliances are connected in parallel so each gets 220 V.

Electromotive Force (EMF) and Internal Resistance

A battery has an electromotive force (emf) epsilon - the energy it gives per unit charge. But batteries also have internal resistance r (due to the electrolyte and electrodes). The terminal voltage V = epsilon - Ir (when discharging). When current flows, some voltage drops across the internal resistance. This is why a battery's voltage drops under load - a 12 V car battery might read 11 V when starting the engine (high current drawn). When no current flows (open circuit), terminal voltage = emf. A good battery has low internal resistance. As batteries age, internal resistance increases, and terminal voltage drops more under load.

Kirchhoff's Laws

Kirchhoff had two simple but powerful rules. Kirchhoff's Current Law (KCL): at any junction, the sum of currents entering equals the sum of currents leaving. Current cannot pile up - like water in pipes. Kirchhoff's Voltage Law (KVL): the sum of all voltage gains (from batteries) around any closed loop equals the sum of all voltage drops (across resistors). The algebraic sum of all potential differences in a closed loop is zero. These laws allow you to analyze any circuit, no matter how complex. Steps: identify junctions and loops, assign current directions (if wrong, answer will be negative), apply KCL at junctions, apply KVL around loops, solve the resulting equations.

Wheatstone Bridge

The Wheatstone bridge is a clever circuit to measure an unknown resistance. Four resistors are arranged in a diamond shape with a galvanometer in the middle. When the bridge is balanced (no current through galvanometer), the ratio of two adjacent resistors equals the ratio of the other two: P/Q = R/S. If P, Q, R are known, S = (Q/P) R. The bridge is balanced by adjusting one known resistor until the galvanometer shows zero deflection. This is a null method - no calibration of the galvanometer needed, just detection of zero current. The meter bridge is a practical version using a 1 m wire as one pair of resistors.

Electrical Power and Energy

Power in a circuit: P = VI = I^2R = V^2/R. Unit: watt (W). A 100 W bulb on 220 V draws about 0.45 A. The energy consumed is power x time. Your electricity bill measures kilowatt-hours (kWh). 1 kWh = using 1000 W for 1 hour = 3.6 x 10^6 J. The heat produced in a resistor is I^2 R t (Joule's law of heating). That is how electric heaters, toasters, and incandescent bulbs work - current passing through a high-resistance wire generates heat. In bulbs, the filament (tungsten) gets so hot it glows white-hot. The heating effect is also why fuses work - if current exceeds rated value, the fuse wire melts, breaking the circuit and protecting appliances.

Key Points

  • •Current I = dQ/dt. Unit: ampere. Conventional current direction opposite to electron flow.
  • •Drift velocity v_d = I/(neA). Very slow (~10^-4 m/s) despite fast random electron motion.
  • •Ohm's law: V = IR. R depends on material, length, area: R = rho L/A.
  • •Resistivity rho: conductor low (Cu: 1.7 x 10^-8), insulator very high, semiconductor intermediate.
  • •Temperature dependence: R_T = R_0 (1 + alpha T). Metals: alpha positive. Semiconductors: alpha negative.
  • •Series: R_eq = sum(R_i). Same I. Parallel: 1/R_eq = sum(1/R_i). Same V.
  • •EMF epsilon: energy per charge from battery. Terminal voltage V = epsilon - Ir.
  • •Kirchhoff's Current Law: sum I_in = sum I_out at junction.
  • •Kirchhoff's Voltage Law: sum of potential differences in closed loop = 0.
  • •Wheatstone bridge balanced: P/Q = R/S. Null method for measuring unknown resistance.
  • •Electrical power P = VI = I^2R = V^2/R. Energy = P x t. 1 kWh = 3.6 x 10^6 J.
  • •Joule's law of heating: H = I^2 R t. Heat produced is proportional to I^2, R, and t.
  • •Internal resistance causes terminal voltage to drop when current is drawn.

Practice Questions

  • Define drift velocity. Derive the expression for current in terms of drift velocity.
  • State Ohm's law. A wire of length 1 m, radius 0.5 mm has resistance 5 O. Find resistivity.
  • Explain temperature dependence of resistance for metals and semiconductors.
  • State Kirchhoff's laws. Find the current in each branch of a given circuit using KCL and KVL.
  • Describe principle and working of Wheatstone bridge. How is meter bridge used to find unknown resistance?
  • An electric bulb rated 60 W, 220 V is connected to 220 V supply. Find current drawn and resistance.
  • A 12 V battery has internal resistance 0.5 O. Find terminal voltage when it supplies 2 A current.
  • Resistors 2 O, 3 O, and 6 O are in parallel. Find equivalent resistance. If connected across 12 V, find total current.