“Slow electrons, fast signal”
Drift velocity
Electrons drift at a few millimetres per second, yet the bulb lights instantly, because the electric field travels at nearly the speed of light and pushes every electron at once.
Class 12 Physics · Gujarat Board, CBSE, GUJCET, JEE and NEET
Current Electricity formulas
Current electricity is the most predictable scoring chapter of Class 12. Ohm's law, the two Kirchhoff rules and the Wheatstone bridge cover almost every question, and the potentiometer results are standard derivations worth memorising outright.
16 formulas, 3 memory hooks, and the 5 mistakes that cost the most marks.
Current and resistance
| What | Formula | Symbols and notes |
|---|---|---|
| Electric current | I = Q/t = neAvd | n is the free electron density, vd the drift velocity |
| Drift velocity | vd = eEτ/m = I/neA | τ is the relaxation time; a few millimetres per second |
| Ohm's law | V = IR | holds for metals at constant temperature |
| Resistance of a wire | R = ρL/A | ρ is resistivity, a property of the material |
| Resistivity and temperature | ρt = ρ₀(1 + αΔT) | α is positive for metals, negative for semiconductors |
| Conductivity | σ = 1/ρ = ne²τ/m | unit siemens per metre |
Circuits
| What | Formula | Symbols and notes |
|---|---|---|
| Resistors in series | R = R₁ + R₂ + … | same current through each |
| Resistors in parallel | 1/R = 1/R₁ + 1/R₂ + … | same voltage across each |
| EMF and terminal voltage | V = E − Ir | r is the internal resistance of the cell |
| Kirchhoff's junction rule | ΣI = 0 at a junction | conservation of charge |
| Kirchhoff's loop rule | ΣV = 0 around a loop | conservation of energy |
| Power | P = VI = I²R = V²/R | choose the form that uses what you are given |
Bridges and the potentiometer
| What | Formula | Symbols and notes |
|---|---|---|
| Wheatstone bridge, balanced | P/Q = R/S | no current flows through the galvanometer |
| Metre bridge | R/S = l/(100 − l) | l is the balancing length in centimetres |
| Potentiometer, comparing EMFs | E₁/E₂ = l₁/l₂ | balancing lengths compared directly |
| Internal resistance by potentiometer | r = R(l₁ − l₂)/l₂ | l₁ open circuit, l₂ with resistance R across the cell |
Taught by Darshit Bhatt, founder and lead faculty at Darshit Sir Institute. Instrumentation and Control engineer, with a master's degree and a chartered degree, teaching in Paldi, Ahmedabad since 2006.
Know the formula but not when to use it?
Darshit Sir has taught this in Paldi since 2006, in the classroom and live online.
Memory hooks
How to remember this chapter.
“Junction is charge, loop is energy”
Kirchhoff's two rules
The junction rule is conservation of charge; the loop rule is conservation of energy. Naming which one you are using earns the mark in a derivation.
“A potentiometer draws nothing”
Why it beats a voltmeter
At balance no current is drawn from the cell, so it measures true EMF. A voltmeter always draws a little current and reads terminal voltage instead.
Where marks go
The mistakes that cost the most.
- Using V = IR across a cell without subtracting Ir. The terminal voltage is less than the EMF whenever current flows.
- Adding parallel resistances directly. It is the reciprocals that add, and the result is smaller than the smallest of them.
- Thinking resistance and resistivity are the same. Cutting a wire in half halves its resistance and changes its resistivity not at all.
- Forgetting that a semiconductor's resistance falls as temperature rises, the opposite of a metal.
- Using the metre bridge formula with the balancing length measured from the wrong end.
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