Elementary Concepts

(1) Resistance (R) & Resistivity (ρ):
R = 1/G where, G = Conductance
$$R = ρ l/a$$
l = length
a = area of cross section
Extra: Volume = a x l

(2) Resistances in Series:
$$R_T = R_1 + R_2 + R_3 + …$$
where, $R_T$ = Effective Resistance

(3) Resistances in parallel:
$$ 1/R_T = 1/R_1 + 1/R_2 + 1/R_3 + ….. $$

Note : $ R_T = {R_1 R_2}/{R_1 + R_2} $

(4) Ohm’s Law:

$$V = I R$$

where, V = voltage

  I = current

  R = resistance

(5) Resistance Temperature Coefficient (R.T.C.):

RTC at t°C = $α_t = {∆R\text" per °C"}/{R_t}$
$$ α_n ={\text" Slope of the characteristics"}/{R_n} $$
e.g. of Slope = ${R_2 – R_1}/{t_2 – t_1}$

(6) $ R_{final}=R_{initial} (1+α_{initial}∆t) $
$R_{t2} = R_{t1} (1+α_{t1}∆t)$

(7) Effect of temperature on RTC:
$$ α_t = α_0(1-α_t t) $$
$$ α_0 = α_t (1 + α_0 t) $$

(8) Temperature coefficient of resisitivity:
$$ ρ_{t2} = ρ_{t1} [1 + α_{t1} (t_2 – t_1) ] $$

(9) RTC of composite conductor:
$$ α = {R_1 α_1 + R_2 α_2}/{R_1 + R_2} $$

(10) Insulation resistnace of a cable:
$$ R_i = {ρ}/{2πl} log_e [R_2/R_1] $$

$R_1$ = Radius of conductor
$R_2$ = Radius of cable incl. conductor and insulator

(11) Thermal Systems:
Joule’s law:
Heat energy = V I t

Calories:
1 calorie = 4.1869 Joules
1 kWh = 3.6 x $10^6$ J
1 kWh = 860 kcal

Heat capacity = $Q/{T_2 – T_1}$

Specific heat, S = $ Q/{m(T_2 – T_1)} $

Sensible heat = m S ∆t

Latent Heat = m x L Joules

Total Heat = Sensible heat + Latent heat

(12) Electrical System:

Electric work, W = Q x V Joules
But, I = Q/t
W = V x I x t Joules

Power, P = V x I

$P = V^2/R watt$

$P = I^2 R$

Energy = Power (P) x Time (t) watt-second/Joules

Note: 1 Newton – metre = 1 Joule = 1 Watt – sec

(13) Efficiency of system:
$$ η = {\text"Output energy"}/{\text"Input energy"} x 100% $$