Electricity Fundamental Equations

8/8/2019 Electricity Fundamental Equations

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CIRCUIT FUNDAMENTALS

VOLTAGE AND CURRENT

The chemical activity of the battery will absorb the electrons at the positive terminal and will maintain a steady

supply of electrons at the negative terminal.

Current directed flow of charge 1 Ampere = 1 coulomb/second

Voltage work per unit charge 1 Volt = 1 joule/coulomb

Power work done in a given amount of time 1 Watt = 1 joule/second

Charge force that causes two particles to be attracted to or repelled from each other

Charge of an electron --- 1.6 x 10-19 coulombs;

o The coulomb is the charge through any cross section of a conductor in one second by anunvarying current of one ampere.

o Practically, one coulomb is about the charge through a 100-W electric lamp.

RESISTANCE

R = L/A (at constant temperature)

where = resistivityL = lengthA = cross-sectional area

V = E/Q

I = Q/t

P = E/t


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Volume = area x length

Volume resistivity resistance of a specified volume of an element or compound

Specific resistance resistance offered by a unit cube of a material

R = L/A R = L/A

= (V/A)/A = L/(V/L)

R = V/A2 R = L2/V

CONDUCTOR SIZES

mil = one-thousandth of an inch

By definition,a wire with a diameter of 1 mil has an area of 1 circular mil (CM), as shown

circular mil = unit of area found by squaring the diameter in mils= cross sectional area of a circle whose diameter is 1 mil

One square mil was superimposed on the 1-CM area of the figure above to clearly show that the square mil has a

larger surface area than the circular mil.

Table 1.0 RESISTIVITY RATINGS OF SOME COMMON ELEMENTS (20C)

Element Resistivity

-CM /ft -cm

Silver 9.90 1.645 x 10-6Copper 10.37 1.723 x 10-6

Gold 14.70 2.443 x 10-6Aluminum 17.00 2.825 x 10-6

Iron 74.00 12.299 x 10-6

Carbon 2.1x104 3.5 x 10-3


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TEMPERATURE EFFECTS

The resistance of most materials used in electrical systems, increases with an increasein temperature.

Temperature coefficient of resistance rating which indicates that resistance varies with temperature ohmic change per degree per ohm at some specified temperature

R1/ R2 = (T+t1) /(T+t2) t1 = 1/(T+t1) t = t2-t1

R2/ R1 = 1+ t1(t)

Tinferred absolute temperature; the temperature through which a straight-line approximation for the actual resistance-versus-temperature curve will intersect the temperature axis.

The temperature at which

all molecular motion

ceases;_273.15C or 0K .


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CONDUCTANCE

By finding the reciprocal of the resistance of a material, we have a measure of how well thematerial will conduct electricity. The quantity is called conductance, has the symbol G, andis measured in Siemens (S).

Conductance measure of the materialsabilityto conduct electric current;equal to the reciprocalof resistance

G = 1/R G = ( A) /L = 1 /


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Problems:

1) How many electrons does a coulomb of charge consist?

2) If 21.847 x 1018 electrons pass through a wire in 70 ms, find the current.

3) Find the current in amperes if 650 C of charge pass through a wire in 50 s.

4) If the potential difference between two points is 36 V, how much work is required tobring 5C of charge from one point to another.

5) The potential difference between two points in an electric circuit is 24 V. If 0.4 J ofenergy were dissipated in a period of 5 ms, what would the current be between thetwo points?

6) An aluminum conductor having a cross sectional area of 1843 MCM is used to transmitpower from a high-voltage dc (HVDC) generating station to a large urban center. If thecity is 900 km from the generating station, determine the resistance of the conductorat the temperature of 20C.

7) Determine the resistance of 1500 feet of annealed copper wire having a diameter of0.23 inch. The resistivity of copper is 1.724 cm at 20C.

8) A kilometer of wire having a diameter of 11.7 mm and a resistance of 0.031 ohm isdrawn such that its diameter is 5mm. What does its resistance become?

9) Determine the cross-sectional area in circular mils of a wire having the followingdiameters:a. 0.159 centimeterb. 0.5000 inchc. 2500 mils

10)The high-voltage dc transmission line mentioned in (6) must be able to operate over awide temperature range. Calculate the resistance of the line at temperatures of -40Cand 40C.

11)An aluminum wire has a resistance of 20 ohms at room temperature (20C). Calculatethe resistance of the same wire at temperatures of -40C, 100C and 200C. Whatconclusion(s) can you derive from the difference in the resistance values?

12)Determine the conductance of 200 feet of aluminum bus bar (at a temperature of20C) which has a cross-sectional area of 4.0 inches by 0.25 inch. If the temperaturewere to increase, what would happen to the conductance of the bus bar?

( = 2.825 x10-6-cm)

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Electricity Fundamental Equations