Current Electricity

Focus: Electric current, drift velocity, resistance, Kirchhoff’s laws, heating effect, and chemical effects of current (JEE Main).

1) Electric Current

• Electric current is the rate of flow of charge.
• Average current: I = ΔQ / Δt
• Instantaneous current: I = dQ / dt
• SI unit: Ampere (A)
• Conventional current flows opposite to electron motion.

I = ΔQ / Δt
I = dQ / dt
  

2) Current Density

• Current density is current per unit area.
• Vector quantity, direction of conventional current.

j = I / A
j = nqvd
  

3) Drift Velocity

• Electrons drift opposite to electric field.
• Drift velocity is very small.

vd = eEτ / m
I = neAvd
  

4) Mobility

• Mobility is drift velocity per unit electric field.

μ = vd / E
  

5) Ohm’s Law

• Current is directly proportional to voltage at constant temperature.

V = IR
j = σE
  

6) Resistance, Resistivity & Conductivity

• Resistance depends on length and area.
• Resistivity depends on material and temperature.

R = ρl / A
σ = 1 / ρ
  

7) Temperature Dependence of Resistance

R(T) = R0[1 + α(T − T0)]
ρ(T) = ρ0[1 + α(T − T0)]
  

8) Combination of Resistors

Rs = R1 + R2 + R3
  

1/Rp = 1/R1 + 1/R2 + 1/R3
  

9) EMF and Internal Resistance

I = E / (R + r)
  

10) Grouping of Cells

I = nE / (R + nr)
  

I = E / (R + r/n)
  

11) Kirchhoff’s Laws

• Junction Law: ΣI = 0
• Loop Law: ΣIR = ΣE

12) Wheatstone Bridge (Balanced Condition)

P/Q = R/S
  

13) Potentiometer

• Used to measure emf accurately.

ε ∝ l
ε1/ε2 = l1/l2
  

14) Heating Effect of Current

H = I²Rt
  

15) Electric Power

P = VI
P = I²R
P = V² / R
  

16) Thermoelectric Effects

• Seebeck Effect
• Peltier Effect
• Thomson Effect

17) Chemical Effect of Current

m = ZIt
F = 96500 C