CBSE Class 12 Physics Current Electricity Formula

Specification

Formula

Electric current

I = Q/t (in ampere)

where I = electric current, Q = Charge flow, t = time taken to flow charge

Current Density

j = I/A =nevd (in ampere/metre2)

where  j = current density, I = current, A = cross-section area of the conductor

Drift velocity of free electrons

vd  = aτ = $\frac{eE}{m}τ$ (m/s)

where a = acceleration, τ = relaxation time, e = charge of electron, E = electric field, m = mass of electron

Relaxation time

τ = $\frac{𝜆}{v_{rms}}$

Where 𝜆 = mean free path of an electron

Mobility of an electron

μe = $\frac{j}{neE}$ (in m2V-1s-1)

Electric resistance

R = tan ፀ = V/I (in ohm or volt/ampere)

Resistance of a wire of length l and cross-section A

R = $\frac{m}{ne^{2}τ}$ . $\frac{l}{A}$

Electrical resistivity or Specific resistance

ρ = R(A/l) = $\frac{m}{ne^{2}τ}$ (in ohm-metre)

Equivalent resistance

1. Resistance in series 

R = R1+R2 +R3 +R4 +..........RN 

2. Resistance in parallel

$\frac{1}{R}$ = $\frac{1}{R_{1}}$ + $\frac{1}{R_{2}}$ + $\frac{1}{R_{3}}$.....$\frac{1}{R_{N}}$

Electric power

P = VI = I2R = $\frac{V^{2}}{R}$ (in watt)

EMF (Electromotive force)

E=dW/dQ (in volt or joule/coulomb)

Relation between EMF, Voltage, and Resistance of a circuit

E = I (R+r)

where R = external resistance and r = internal resistance

Electric cell

E = $\frac{W}{Q}$ . V = $\frac{W_{ext}}{Q}$ = IR

Combination of cells

In series  I = $\frac{nE}{nr + R}$ 

In parallel I = $\frac{nE}{r + nR}$ 

In mixed grouping I = $\frac{mnE}{nr + mR}$ 

Combination of cells

For maximum current

R = $\frac{nr}{m}$   , Imax = $\frac{1}{2}$ . $\frac{mE}{r}$

Krirchhiff’s laws

ΣI = 0, ΣIR = ΣE

Wheatstone bridge

$\frac{P}{Q}$ = $\frac{R}{S}$

Metre bridge

$\frac{P}{Q}$ = $\frac{l}{100 - l}$

Potentiometer

E = Kl, $\frac{E_{1}}{E_{2}}$ = $\frac{l_{1}}{l_{2}}$, r= R($\frac{l_{1}}{l_{2}}$ - 1)