# 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 (a^{2})

### Series Circuits

U_{AB} = U_{1}= U_{2} = .... = U_{n}

I_{AB} = I_{1}= I_{2} = .... = I_{n}

R_{AB} = R_{1}= R_{2} = .... = 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

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