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CLASS 12 • PHYSICS
Current Electricity
1. Drift Velocity Basics
Current Relation (IMPORTANT)
$I = neAv_d$
Drift Velocity
$v_d = \frac{eE}{m}\tau$
$\tau$ = Relaxation Time
Current Density
$J = \frac{I}{A} = ne v_d$
Mobility
$\mu = \frac{v_d}{E}$
2. Ohm's Law & Resistance
Vector Form
$\vec{J} = \sigma \vec{E}$
$\sigma$ = Conductivity
Resistance
$R = \rho \frac{L}{A}$
Temp. Dependence
$R_t = R_0(1 + \alpha \Delta T)$
Conductance
$G = 1/R$ and $\sigma = 1/\rho$
3. Resistor Combinations
Series
$R_s = R_1 + R_2$
Current Same, V divides
Parallel
$\frac{1}{R_p} = \frac{1}{R_1} + \frac{1}{R_2}$
Voltage Same, I divides
Power Dissipated
$P = VI = I^2R = \frac{V^2}{R}$
4. Cells & Internal Resistance
Terminal Voltage (Discharging)
$V = E - Ir$
Note: $V < E$
Terminal Voltage (Charging)
$V = E + Ir$
Note: $V > E$
Cells in Series
$E_{eq} = E_1 + E_2$
Cells in Parallel
$E_{eq} = \frac{E_1 r_2 + E_2 r_1}{r_1 + r_2}$
5. Kirchhoff's Laws
Junction Law (KCL)
$\sum I_{in} = \sum I_{out}$
Conservation of Charge
Loop Law (KVL)
$\sum \Delta V = 0$
Conservation of Energy
Wheatstone Bridge (Balanced)
$\frac{P}{Q} = \frac{R}{S}$
Current in galvanometer = 0
6. Measuring Instruments
Meter Bridge (Unknown R)
$R = S (\frac{l}{100-l})$
Potentiometer Principle
$V \propto l \Rightarrow V = kl$
Compare EMFs
$\frac{E_1}{E_2} = \frac{l_1}{l_2}$
Internal Resistance (r)
$r = R (\frac{l_1}{l_2} - 1)$
Most important practical formula
7. Common Exam Traps
- ⚠️ Alloy vs Metal: Alloys (Nichrome, Manganin) have HIGH resistance but LOW temp coeff ($\alpha$). Metals have LOW resistance but HIGH $\alpha$.
- ⚠️ KVL Sign: Moving with current across resistor = $-IR$. Moving against current = $+IR$. Moving $-$ to $+$ in battery = $+E$.
- ⚠️ Open Circuit: When circuit is open ($I=0$), Terminal Voltage $V = E$ (EMF).
8. Golden Theory Rules
- Why Potentiometer? It draws ZERO current at null point, so it measures exact EMF (Voltmeter draws current, so it measures $V < E$).
- Series Bulbs: In Series, the bulb with HIGHER resistance glows brighter ($P=I^2R$).
- Parallel Bulbs: In Parallel (House), bulb with LOWER resistance glows brighter ($P=V^2/R$).
