Electrical Quantities.
AC circuit.
The instantaneous voltage of a sine wave is given by VI = Vmax*sin2pft
Resistance.
The current in a circuit is proportional to the circuit voltage and inversely proportional to the circuit
resistance at constant temperature.
Resistance in series in a circuit is added together to find the total resistance Rt = R1 + R2 + R3 etc
Resistance in parallel is worked out slightly differently 1/RT = 1/R1 + 1/R2 + 1/R3
Resistance of a cable.
resistance = (resistivity * length) / area R =r(l/a)
Example
What is the resistance of a length of cable 50 metres long with a csa of 2.5mm2 and a resistivity of 17.6
mW mm
R =(rl)/a ((17.6x10-6)x(50x103))/2.5 = 0.352 ohms
Capacitance.
In a parallel circuit CT = C1 + C2 + C3
In a series circuit 1/CT = 1/C1 + 1/C2 + 1/C3
Example
What is the total capacitance in a/. A parallel circuit. and b/. A series circuit both containing three
capacitors C1 = 5 Farads C2 = 10 Farads C3 = 15 Farads
a/. CT = C1 + C2 + C3 = 5+10+15 = 30 Farads
b/. 1/CT = 1/C1 + 1/C2 + 1/C3 = 1/CT = (1/5)+(1/10)+(1/15) = 0.2+0.1+0.0666 = 0.3666 so CT = 2.727
Capacitive reactance.
capacitive reactance Xc = 1/(2pfC)
Temperature coefficient.
symbol a, unit W per W per 0C
Resistance changes with change of temperature
Temperature coefficient – If we were to take a sample of conductor that has a resistance of 1W at a
temperature of 0C, and then increase its temperature by 1 0C the resulting increase in resistance is
it’s temperature coefficient. An increase of 2 0C would result in twice the increase, and so on.
Copper’s temperature coefficient is taken as 0.004 W/W/0C.
final resistance = RF = R0(1 + at)
where R0 = resistance at 0 0C
a = temperature coefficient
t = change in temperature
for change in temperature between any two values the formula is
R2 = (R1(1+at2))/(1+at1)
where R2 = final resistance
t1 = initial temperature
t2 = final temperature
for most common conducting materials the temperature coefficient ranges from 0.0039 to 0.0045 W/W/ 0C
that of copper being taken as 0.004 W/W/ 0C
Example
R0 = 10 W, t = 50 0C, a = 0.004
RF = R0(1 + at) = 10(1 + 0.004 * 50) = 12 W
Example
R1 = 200 W , t1 = 20 0C, t2 = 600 0C, + a = 0.0045 W/W/ 0C
R2 = (R1(1 + at2))/(1 + at1) = 678.899 W
Power.
symbol = P, unit = watt (W)
Power in an a.c. circuit is affected/determined by the resistance, capacitance and inductance of the circuit.
The power used to do useful work is called the True Power, it is the rate at which energy is used and is
measured in watts.
V*I is the apparent power, it has to be multiplied by the power factor (pf)(cos q) to give watts.
Apparent power = (V * I) or (P = I2 * R or (P = V2/R)
True power = V * I * cosq)
(with a 3phase supply – true power = V * I * pf * 1.732)
Power is the rate at which energy is converted P = energy/time
Electrical energy.
symbol = E, unit = joule, 1joule = 1Watt second
normally measured in KWh
E = V * I * t
Water heating.
Joule in his experiments showed that 4.2 J of electrical energy = one calorie of heat energy.
Hence it required 4.2 J of electrical energy to raise the temperature of one gram of water through 1 0C.
This value is called the specific heat of water.
Example
How long will it take a 2kW 240 volt kettle to raise the temperature of 2 litres of water from 8 0C to
boiling point? Assume 100% efficiency (SH of water = 4.2J/kg/0C and 1 litre of water has a
mass of 1kg)
KWhoutput = ((mass*change in temp*SH)/(time)) = ((2000*92*4.2)/(3600000)) = 0.215kWh
As 100% efficiency is assumed input = output then 2kW x hours = 0.215kWh
So hours = (0.215/2) = 0.1075 hours = 6.45 minutes
Efficiency.
Percentage efficiency = (output/input)*100
Example
Calculate the efficiency of a water heater if the output in kilowatt hours is 24kWh and the input
energy is 30kWh.
Efficiency = (24/30)*100 = 80%
Coulomb.
symbol Q
The quantity of electricity that passes a point in a circuit in a certain time. One coulomb is said to
have passed when 1 ampere flows for 1 second.
Q = I * T
Inductance of a coil.
L = NF/I
where L is in Henry's
N = number of turns
F = magnetic flux(T*m2)
I = current (A)
Inductive reactance.
XL = 2pfL where L = henry's
Flux density.
symbol B, unit tesla (T)
Flux density is measured in flux per m2 or Wb/m2. This unit however is known as
the tesla (T).
B(T) = (F(Wb))/(a(m2))
Example
A motor field pole has an area of 60cm2. If the pole carries a flux of 0.3Wb, calculate the
flux density.
F = 0.3 Wb a = 60cm2 or 0.006m2
B = F/a = 0.3/0.006 = 50T
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