Electric Current Through Conductors
Easy Overview
Imagine a wire as a pipe full of electrons. When you push them from one end, they all move — that's electric current. This chapter is about how current flows through conductors, why some materials resist it more than others, and how circuits work. It's the physics behind every electronic device: from a simple flashlight to your phone charger.
Electric Current — Flow of Charge
Current I = Q/t — the rate at which charge flows past a point. Measured in amperes (A). 1 A = 1 C/s. By convention, current direction is the flow of positive charge (from + to −), even though electrons actually move the other way. Current density J = I/A, where A is cross-sectional area. In metals, free electrons drift slowly (mm/s) but the electric signal propagates at nearly light speed — like a hose filling instantly even though water molecules move slowly.
Ohm's Law and Resistance
V = IR — the voltage across a conductor is proportional to the current through it, as long as temperature is constant. R is resistance (in ohms, Ω). Resistance depends on the material: R = ρL/A, where ρ is resistivity (a material property). Conductors have low ρ (copper: 1.7×10⁻⁸ Ω·m), insulators have very high ρ. Resistivity increases with temperature for metals (ρ = ρ₀[1 + α(T − T₀)]). Conductance G = 1/R, measured in siemens (S).
Combinations of Resistors
Series: same current through all resistors, voltage divides. R_eq = R₁ + R₂ + R₃ + ... If one bulb in a series string blows, all go out. Parallel: same voltage across all resistors, current divides. 1/R_eq = 1/R₁ + 1/R₂ + 1/R₃ + ... Parallel is how your home is wired — each appliance gets full voltage, and turning one off doesn't affect others. For two resistors in parallel: R_eq = (R₁R₂)/(R₁+R₂).
Electromotive Force (EMF) and Internal Resistance
A battery isn't perfect — it has internal resistance r. The terminal voltage V = ε − Ir, where ε is the EMF (theoretical voltage with no load). As you draw more current, terminal voltage drops because of Ir drop. That's why a car's headlights dim when you start the engine — starter motor draws huge current, voltage dips. When the battery is old, internal resistance increases, and it can't deliver enough current.
Kirchhoff's Laws — Circuit Solving
Kirchhoff's Current Law (KCL): the sum of currents entering a junction equals the sum leaving. Conservation of charge. Kirchhoff's Voltage Law (KVL): the sum of voltage drops around any closed loop equals the sum of EMFs in that loop. Conservation of energy. These two laws let you solve any circuit, no matter how complex. Assign currents, write KCL at junctions, write KVL for loops, solve the equations.
Key Points
- •Current I = Q/t, measured in amperes
- •Ohm's law: V = IR (at constant temperature)
- •Resistance R = ρL/A, where ρ is resistivity
- •Series: R_eq = R₁ + R₂ + ..., same current
- •Parallel: 1/R_eq = 1/R₁ + 1/R₂ + ..., same voltage
- •EMF ε = terminal voltage when no current flows
- •Terminal voltage V = ε − Ir (r = internal resistance)
- •KCL: ΣI_in = ΣI_out; KVL: Σε = ΣIR in a loop
Practice Questions
- A wire of resistance 5 Ω is stretched to double its length. Find new resistance.
- Three resistors 2 Ω, 3 Ω, and 6 Ω are connected in parallel. Find equivalent resistance.
- State and explain Kirchhoff's laws with an example circuit.
- A battery of EMF 12 V and internal resistance 1 Ω is connected to a 5 Ω resistor. Find current and terminal voltage.