Current Electricity takes the static charges of Electrostatics and sets them moving through a circuit, replacing field-and-potential diagrams with the more immediately practical language of current, resistance and circuit analysis.
Ohm's law is this chapter's starting point, but real circuit problems rarely reduce to that one equation alone — that's what Kirchhoff's two laws are for. The junction rule is charge conservation applied to a circuit node; the loop rule is energy conservation applied around any closed path. Together they let you solve circuits too complicated for simple series-parallel reduction, including the Wheatstone bridge, one of this chapter's most frequently tested applications.
Core current electricity formulae
| Quantity | Formula |
|---|---|
| Ohm's law | V = IR |
| Resistivity and resistance | R = ρl/A |
| Resistors in series | R = R₁ + R₂ + ... |
| Resistors in parallel | 1/R = 1/R₁ + 1/R₂ + ... |
| Kirchhoff's junction rule | ΣIin = ΣIout |
| Kirchhoff's loop rule | ΣV = 0 around any closed loop |
| Wheatstone bridge balance condition | P/Q = R/S |
| Electrical power | P = VI = I²R = V²/R |
| Terminal voltage of a cell | V = ε − Ir |
Topics covered
- Electric current and drift velocity — the microscopic picture of current as moving charge carriers
- Ohm's law and resistivity — and why some materials, called non-ohmic conductors, don't obey it
- Temperature dependence of resistance — different behaviour in metals versus semiconductors
- Resistors in series and parallel — and combined networks requiring systematic reduction
- Kirchhoff's laws — the junction rule and loop rule, and how to apply both to solve multi-loop circuits
- Wheatstone bridge — the balance condition, and its use in accurately measuring an unknown resistance
- Potentiometer — how it measures EMF and potential difference without drawing current from the source
- EMF, internal resistance and terminal voltage — the practical distinction between a cell's rated EMF and what a circuit actually sees
- Electrical energy and power — and the heating effect of current
Why this chapter matters
In NEET and JEE, Kirchhoff's law-based multi-loop circuit problems and Wheatstone bridge numericals are consistently among the most frequently repeated question types across years, precisely because they test systematic problem-solving rather than formula recall. Potentiometer-based comparison-of-EMF questions are a close second in frequency.
For Class 12 boards, expect a full Kirchhoff's law circuit-solving numerical and a derivation or application question on the Wheatstone bridge or potentiometer.
Mistakes students make in this chapter
- Assigning current directions arbitrarily and then panicking at a negative answer. A negative result from Kirchhoff's laws simply means the actual current flows opposite to your assumed direction — it's not an error, and the magnitude is still correct.
- Applying series-parallel reduction to a circuit that genuinely needs Kirchhoff's laws. Once a circuit has more than one EMF source or a bridge-like structure, simple series-parallel reduction no longer works and the full Kirchhoff's law method is required.
- Confusing EMF with terminal voltage. EMF is the cell's maximum potential difference with no current drawn; terminal voltage is always slightly lower once current flows, due to the cell's own internal resistance.
- Forgetting the Wheatstone bridge balance condition only holds at balance. The galvanometer shows zero deflection only when P/Q = R/S exactly — away from balance, the bridge requires full Kirchhoff's law analysis, not the simple ratio.
- Believing a potentiometer draws current from the cell being measured. Its entire advantage is measuring EMF at the null point, where no current is drawn from the source being tested — this is precisely why it's more accurate than a voltmeter for this purpose.
Worked example: maximum power, and why efficiency is only 50%
- Write the current first. Internal resistance sits in series with R, so the full loop resistance is (R + r):I = ε / (R + r) = 12 / (R + 2)
- Write the power delivered to R. Only R gets this — the rest heats the battery itself.P = I²R = ε²R / (R + r)²
- Maximise it. Differentiate with respect to R and set dP/dR = 0. The numerator gives (R + r)² − 2R(R + r) = 0, which simplifies to (R + r) − 2R = 0:R = r = 2 Ω
- Substitute back for the maximum power.P_max = ε²/4r = 144 / 8 = 18 W
- Now check the efficiency. At R = r the current is I = 12/4 = 3 A, so the battery's total power output is εI = 36 W, while R receives 18 W and the internal resistance wastes the other 18 W:η = P_R / P_total = 18 / 36 = 50%
What the notes contain
The PDF works through Kirchhoff's law circuit-solving methodically for two- and three-loop circuits, derives the Wheatstone bridge balance condition from the loop rule, and explains the potentiometer's null-point method with a fully worked EMF-comparison numerical.
How to use this: build the concept from these notes first, then do one quick NCERT pass before the exam for exact wording and diagram labels, and spend whatever time is left on previous year questions.
Questions
What do Kirchhoff's junction and loop rules actually represent physically?
The junction rule is charge conservation — whatever current flows into a junction must flow out. The loop rule is energy conservation — the total potential change around any closed loop is zero. Both are explained with the underlying physical reasoning, not just stated as rules.
Why is a potentiometer more accurate than a voltmeter for measuring EMF?
At its null point, a potentiometer draws no current at all from the cell being measured, so there's no voltage drop across internal resistance to introduce error. A voltmeter always draws some current, however small, which slightly reduces the measured value.
Does this cover the Wheatstone bridge derivation?
Yes, derived from Kirchhoff's loop rule applied to the bridge circuit, arriving at the balance condition P/Q = R/S with the full reasoning shown.
Is Kirchhoff's law circuit solving covered with worked examples?
Yes, with a systematic step-by-step method for assigning currents, writing junction and loop equations, and solving the resulting simultaneous equations.
All other chapters
Every chapter of Class 11 and Class 12 Physics, Chemistry and Biology — each with its own notes and PDF.