Chapter 12 – Current Electricity (JEE Physics)
1. Electric Current
Electric current is defined as the rate of flow of electric charge through a conductor.
$$ I = \frac{Q}{t} $$
- SI unit: Ampere (A)
- 1 A = 1 C/s
2. Conventional Current vs Electron Flow
Conventional current flows from positive to negative terminal, whereas electrons move from negative to positive terminal.
3. Drift Velocity
Drift velocity is the average velocity acquired by free electrons in a conductor under the influence of an electric field.
$$ v_d = \frac{I}{nqA} $$
Although electrons move randomly at high speeds, drift velocity is very small.
4. Relation Between Drift Velocity and Electric Field
$$ v_d = \frac{eE\tau}{m} $$
- $\tau$ = relaxation time
- $E$ = electric field
5. Ohm’s Law
At constant temperature, current through a conductor is directly proportional to the potential difference across it.
$$ V = IR $$
6. Resistance
Resistance is the opposition offered by a conductor to the flow of electric current.
$$ R = \rho \frac{L}{A} $$
- $\rho$ = resistivity
- $L$ = length
- $A$ = cross-sectional area
7. Factors Affecting Resistance
- Length of conductor
- Area of cross section
- Material of conductor
- Temperature
8. Temperature Dependence of Resistance
$$ R_T = R_0 (1 + \alpha T) $$
Metals have positive temperature coefficient, semiconductors have negative.
9. Electrical Energy and Power
$$ P = VI = I^2R = \frac{V^2}{R} $$
$$ E = Pt $$
10. Combination of Resistors
Series Combination
$$ R_{eq} = R_1 + R_2 + R_3 $$
Parallel Combination
$$ \frac{1}{R_{eq}} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3} $$
11. Kirchhoff’s Laws
Kirchhoff’s Current Law (KCL)
Algebraic sum of currents at a junction is zero.
Kirchhoff’s Voltage Law (KVL)
Algebraic sum of potential differences in a closed loop is zero.
12. Wheatstone Bridge
Wheatstone bridge is used to accurately measure unknown resistance.
$$ \frac{R_1}{R_2} = \frac{R_3}{R_4} $$
13. Meter Bridge
$$ \frac{R}{S} = \frac{l}{100-l} $$
14. Potentiometer
Potentiometer is used to measure emf and internal resistance of a cell without drawing current.
$$ V \propto l $$
15. EMF and Internal Resistance
$$ V = E - Ir $$
$$ r = \frac{E - V}{I} $$
16. Cells in Series and Parallel
Series: $E_{eq} = nE,\; r_{eq} = nr$
Parallel: $E_{eq} = E,\; r_{eq} = \frac{r}{n}$
17. Maximum Power Transfer Theorem
Maximum power is transferred when:
$$ R = r $$
18. Common JEE Mistakes
- Wrong sign convention in Kirchhoff’s laws
- Ignoring internal resistance
- Incorrect series-parallel reduction
- Confusing emf with terminal voltage
19. Typical JEE Question Areas
| Concept | Weightage |
|---|---|
| Ohm’s Law & Power | High |
| Kirchhoff’s Laws | Very High |
| Potentiometer | High |
| Wheatstone Bridge | Medium |
20. Final Revision Checklist
You have mastered Current Electricity if you can:
- Apply Ohm’s law correctly
- Solve multi-loop circuits using Kirchhoff’s laws
- Use potentiometer formulas confidently
- Handle internal resistance problems
- Calculate power and energy accurately