Current Electricity Made Simple: From Ohm's Law to the Wheatstone Bridge

A friendly, first-principles walk through Current Electricity for CBSE Class 12 — electric current, Ohm's law, resistivity, series and parallel resistors, Kirchhoff's rules and the Wheatstone bridge — with everyday analogies, correct SI units, and a fully worked numerical.

By the PadhoDost Team · 📖 8 min read · Updated 4 August 2026

Part of Class 12 (CBSE) prep

🧠 Water in a pipe

Imagine water flowing through a pipe. The amount of water rushing past a point every second is like electric current. A pump that pushes the water is like a battery providing voltage. And if the pipe is narrow or clogged, the water struggles to flow — that struggle is resistance. Hold this picture in your head, dost — almost everything in Current Electricity is just this water story retold with electrons. Padho, dost, and let's begin!

What exactly is electric current?

SERIES PARALLEL + R1 R2 Series: R = R1 + R2 + R1 R2 Parallel: 1/R = 1/R1 + 1/R2
In a series circuit the current has only one path so the resistances add (R = R1 + R2), while in a parallel circuit the current splits between two branches so 1/R = 1/R1 + 1/R2.

Electric current is the rate of flow of electric charge. In a metal wire, tiny particles called free electrons drift along and carry the charge. If a charge Q passes through any cross-section of a wire in time t, the current is simply how much charge flows per second.

I = Q / t SI unit: ampere (A) = 1 coulomb per second (C/s)

One important convention: the direction of conventional current is taken as the direction in which positive charge would move — which is opposite to the direction in which electrons actually drift. Current is a scalar quantity; it has magnitude but no direction in the vector sense (that is why currents at a junction add up like ordinary numbers).

ℹ️ Electrons drift surprisingly slowly — only a fraction of a millimetre per second! The bulb lights up almost instantly because the electric field is set up along the whole wire at nearly the speed of light, so electrons everywhere start drifting together at once.

Ohm's Law — the golden rule

For many conductors at a constant temperature, the current through them is directly proportional to the potential difference (voltage) across them. The constant of proportionality is the resistance R.

V = I R Resistance R = V / I SI unit: ohm (Ω) = 1 volt per ampere (V/A)

A higher R means it is harder for current to flow for the same voltage. Materials that obey this straight-line relationship (like most metals) are called ohmic; things like diodes and bulb filaments are non-ohmic because their R changes with conditions.

Resistivity — resistance built into the material

Resistance depends on the shape of the wire, not just what it is made of. A long wire resists more; a thick wire resists less. Pulling these geometric factors out leaves us with resistivity (ρ), a property of the material itself that does not depend on size or shape.

R = ρ L / A where L = length, A = cross-sectional area, ρ = resistivity (unit: ohm-metre, Ω·m)

🧠 Why long and thin resists more

Think of a crowded railway platform. A long corridor (large L) means people take longer to get through — more resistance. A wide corridor (large A) lets many people pass side by side at once — less resistance. Copper is like a smooth empty hall (low ρ); rubber is like a wall (huge ρ).

For metals, resistivity increases with temperature — hotter atoms vibrate more and obstruct the drifting electrons. That is why a bulb's filament has a much higher resistance when glowing hot than when cold.

Resistors in series and parallel

When we connect several resistors, we can replace them with a single equivalent resistance. In series (one after another, same current through each) the resistances simply add. In parallel (side by side, same voltage across each) the reciprocals add, and the equivalent is always smaller than the smallest resistor.

FeatureSeriesParallel
ConnectionEnd to end, single pathSide by side, multiple paths
Same for allCurrent IVoltage V
Equivalent RR = R1 + R2 + R31/R = 1/R1 + 1/R2 + 1/R3
Effect on total RIncreases (bigger than any)Decreases (smaller than smallest)

📝 Worked example: two resistors, series then parallel

Given: R1 = 6 Ω and R2 = 3 Ω, connected to a 12 V battery.

SERIES: R_eq = R1 + R2 = 6 + 3 = 9 Ω

Current from battery: I = V / R_eq = 12 / 9 = 1.33 A

PARALLEL: 1/R_eq = 1/6 + 1/3 = 1/6 + 2/6 = 3/6 = 1/2

So R_eq = 2 Ω (note: smaller than 3 Ω, the smaller resistor)

Total current: I = V / R_eq = 12 / 2 = 6 A

Check the branches: I1 = 12/6 = 2 A, I2 = 12/3 = 4 A; sum = 2 + 4 = 6 A. It matches!

Kirchhoff's rules — for circuits Ohm's law can't crack alone

Complex circuits with many batteries and loops need two rules given by Gustav Kirchhoff. They come straight from two conservation laws you already know.

The two rules

  • Junction Rule (KCL): The total current entering a junction equals the total current leaving it. This is just conservation of charge — charge cannot pile up at a point.
  • Loop Rule (KVL): Around any closed loop, the algebraic sum of all changes in potential is zero. This is conservation of energy — return to the start and the potential must be the same.
  • Sign tip: crossing a resistor along the current direction is a drop (−IR); crossing a battery from − to + terminal is a rise (+EMF).
⚠️ Common mistake: forgetting signs in the loop rule. First fix a direction for each current (guess freely — if your answer comes out negative, the current simply flows the opposite way). Then be consistent: potential drops across a resistor in the direction of the current, and follow the battery's terminals carefully.

The Wheatstone Bridge

The Wheatstone bridge is a clever arrangement of four resistors (P, Q, R, S) in a diamond, with a battery across one diagonal and a sensitive galvanometer across the other. By adjusting the resistors until the galvanometer reads zero — the balanced condition — we can find an unknown resistance very accurately without ever measuring the current.

Balanced bridge (no current through galvanometer): P / Q = R / S

At balance, no current flows through the galvanometer, which means the two junctions across it are at the same potential. Applying Kirchhoff's rules to the arms then gives this neat ratio. If three resistances are known, the fourth (unknown) follows instantly — this is the principle behind the metre bridge used in your practical exams.

Quick revision — lock these in

  • Current I = Q/t, measured in amperes (A); conventional current flows opposite to electron drift.
  • Ohm's law: V = IR, valid at constant temperature for ohmic conductors.
  • Resistivity: R = ρL/A; ρ is a material property and rises with temperature in metals.
  • Series adds resistances; parallel adds reciprocals and lowers the total resistance.
  • Kirchhoff: junction rule = charge conservation; loop rule = energy conservation.
  • Wheatstone bridge balances when P/Q = R/S, with zero galvanometer current.

⚡ Quick check

Three resistors of 3 Ω, 3 Ω and 3 Ω are connected in parallel. What is their equivalent resistance?

Ready to test yourself? 🎯

Lock it in with the practice test for this chapter.

Take the practice test →

Keep studying

See all Class 12 (CBSE) study material →