List of formulas related to direct Current

Electric Current

I: current (A), q: charge (C), t: time

$$ I = {\frac{ \Delta q}{ \Delta t}}(A) $$

Ohm's Law

U: electric potential difference between the ends of the resistor R

$$ I = {\frac{U}{R}} $$

Work Created By A Current (Joule's Law)

$$ W = U.I.t = I^2 R $$

Electrical Power

$$ P = U.I = I^2 R $$

Resistance

ρ: resistivity of the material (Ωm), l: length (m), A: cross-section area (a²)

$$ R = \rho \frac{l}{A} $$ $$ R = \rho \frac{U}{l}(\Omega) $$

Series Circuits

U_AB = U₁= U₂ = .... = U_n

I_AB = I₁= I₂ = .... = I_n

R_AB = R₁= R₂ = .... = R_n

Parallel Circuits

$$ U_{AB} = U_1 = U_2 = .... = U_n $$ $$ I_{AB} = I_1 = I_2 = .... = I_n $$ $$ \frac{1}{R_{AB}} = \frac{1}{R_1} = \frac{1}{R_2} = .... = \frac{1}{R_n} $$

Work Or Heat Energy Produced By A Resistor

$$ W = IR^2 t = \frac{U^2}{R} t $$

Power Consumption Of A Resistor

$$ Q = IR^2 = \frac{U^2}{R} $$

Electromotive Force Of An Electrical Generator

W: work of force (J), q: charge(c)

$$ \zeta = \frac{W}{q}(V) $$

Generators In Series

r: internal resistance of the generator

$$ \zeta _b = \zeta _1 + \zeta _2 + .... + \zeta _n $$ $$ r _b = r _1 = r _2 = .... = r _n $$ $$ (\zeta _1 : r _1) = (\zeta _2 : r _2) = .... = (\zeta _n : r _n) $$ $$ \zeta _b = n\zeta $$ $$ r_b = n.r $$

Generators In Parallel

$$ r_b = \frac{r}{n} $$ $$ \zeta _b = \zeta $$

Generators In Series-Parallel

$$ \zeta _b = m\zeta $$ $$ r_b = \frac{m}{n} r $$

Work And Power Of Generator

H: Efficiency of genarator

$$ W _g = \zeta.I.t $$ $$ P _g = \frac{W_g}{t} = \zeta.I $$ $$ H = \frac{U}{\zeta} = \frac{R}{R + r} $$