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A comprehensive overview of dc circuits, covering fundamental concepts such as resistance, network theorems, magnetic fields, inductance, electrostatics, capacitance, and instrumentations. It includes detailed explanations, formulas, and examples to help students understand the principles and applications of dc circuits. Suitable for university or high school students studying electrical engineering or related fields.
Typology: Exercises
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POWERLINE REVIEW CENTER M E Z Z A N I N E F L O O R , D O N A A M P A R O B U IL D IN G C O R N E R E S P A N A & G. M. T O L E N T I N O S T R E E T S S A M P A L O C , M A N I L A T E L. N O S. 7 3 5 - 7 3 - 0 2 & 7 3 3 - 2 1 - 1 8
T E L. N O S. ( 0 3 ) 2 6 1 - 2 2 4 4 & ( 0 3 2 ) 2 6 1 - 8 4 5 2
RESISTANCE ( R )•. It may be defined as that property o f a substance or material which opposes the flow o f electron or current.
The Resistance o f a conductor is given by:
R = p —^ D^^1 = P — = /»-^^ ^ A V r A 2 Where : I = length o f the conductor in m or ft. A = cross sectional area in m 2 , sq. mils or circular mils (CM). A = —d 2 sq. mils ; A = d 2 CM ; if cl = diameter o f the conductor in mils. 4 NOTE : 1 inch = 1000 mils , 1 sq. inch = 10 6 sq. mils , 1 sq. inch = — x 10 6 CM n p = specific resistance or resistivity o f the material o f the conductor in Q-m or Q-CM/ft. = 1.77 x 10 8 Q-m =10.66 Q -C M / ft => for hard-drawn Copper (HDC) @ 20 °C = 1.72 x 10 ~8 Q-m =10.50 Q -C M / ft => for annealed Copper @ 2C °C = 2.83 x 10 "“ Q-m = 17.10 Q -C M / ft for Aluminum @ 20 °C V = volume o f conductor in m 3 or ft3.
The Variation o f Resistance with Temperature is given by : R2 = /? ,[l + a, {t2 - /,)] Where : R2 = resistance @ t 2 , final value o f resistance in Q R} = resistance @ f , , initial value o f resistance in Q ti t t2~ initial and final temperature in °C respectively, o', =temperature coefficient @ f, in °C 1
_a_ = 7 — -— ; T - —— = inferred absolute zero resistance temperature in °C. |r| + <i a T = -234.5 °C for annealed copper, T = -242 °C for HDC, T - - 2 3 6 °C for aluminum.
O H M 'S L A W : it is stated that the ratio o f potential difference (V ) between any two points on a conductor to the current (I) flowing between them, is constant provided the temperature o f the conductor V V does not change. i.e. — = constant or — = R
RESISTANCE in SERIES : RESISTANCE in PAR ALLEL :
y.r = v , + y ,+ V j+- - + y„ v r = Vi = K ,= V, =•■• v„ I, = / , - h ' = In h = h 1 h H j '••• 1 f«
MAGNETIC FIELD : exists in a region o f space if a moving charge there experiences a force (other than Friction ) due to its motion.
The Magnitude o f F orce is given by : F = qvB sin 9 in Newton where : q = the charge magnitude in coul. ( C ), v = the magnitude o f the velocity in m/sec. 0 - the angle between the field lines and the velocity. B = magnetic flux density or magnetic induction in Tesla ( Wb/m 2 ) NOTE : 1 Tesla = 10 4 Gauss = 10 4 lines/cm 2 = 1 N/A-m
F orce on a Current in a M aenetic Field is : In metric : F - BlLsmO in Newton where : B = magnetic induction, Tesla / = current in Amp L = length o f conductor, m 8 - angle between the direction o f / and B. lill.sinO In COS / ' i n dynes 10 where : B ~ in Gauss, / = in Amp , L = in cm , „ c BILsinO. In English : F = --------------- m lbs. 6 11,300, where : B = in lines/in2, / = in Amp, L= in inches
Torque on a Flat Coil in a Uniform M aenetic Field is : t = NIAB sin 6 in N-m where : A/= number o f loops or turns, A = area o f the coil, m 2 0 ~ angle between B and perpendicular to the plane o f the coil NOTE : To determine the direction o f rotation o f the coil use Right - Harnl Rule.
M aenetic Field on a L ons straight wire : B = where : r is the distance to a point from the axis o f the wire. 2 tt 7 '
Maenetic Field on Center o f a Circular coil with N toons'.
B = where : a is the radius o f the circular coil. 2a
Maenetic Field in the Interior point o f a L one Solenoid : N B = / / Q» / where : n is the number of turns per meter - —
Magnetic Field in the interior point o f Toroid with N h o p s : 5 - where : r is the radius o f the circle or, which a point lies. 2 m
Force between Two Parallel Conductors :
f - s 2 x 10~7 2 -~ where : i is the length o f the conductor, and 2nd d d is the distance between conductors
Coulomb '.s' Law o f Magnetic Forces : M 4^p//r r 2
MtM 2 F = - ---------------- - — where : M, & M2 are pole strength in Wb., and
r is the distance between the poles, m.
Faraday's Law o f Electromagnetic Induction (ea t’us. o f Induced em f): A
- Ai = R Aq = B fv x 10~s in volts At At At
H = N
INDUCTANCE (L) : is the property o f A C circuits which opposes any change in the amount o f current, Its unit is Henry. Expression o f S elf Inductance : I - ,^ _ r_ = ... r N<p^ HrVoAN2 »-------^ ln. Henry I I where : A =is the area o f cross section o f the core in m\ <p = is the magnetic flux in Wb, t =is the length o f the core in m (ir = is the relative permeability o f the core
Expression o f Mutual Inductance:
where : k = coefficient o f coupling N, N2 = respective number o f turns Lu!,2 = respective self- inductances o f the two coils.
Inductances in Series : Inductances in Parallel : When M assists Lt & Li When M assists L, & L 2
L — Li 4- L-> ■+■ 2.M L .L t-M 2 L, + L2 - 2 M When M opposes L| & L 2 When M opposes L, & L 2
L = L, + L-, - 2M
L,Z-2 - M 1
O hm ’s Law o f Magnetic Circuits : = = in Weber 9? <n t / A p /H r!* O'* Where : 9? = is the Reluctance o f the magnetic circuit, it is reciprocal o f Permeance Energy Stored in a Magnetic Field : W , = — L I 2 in Joules L 2
Energy Stored in a Magnetic Field per unit Volume: jp _ ---------- B^ ^ jn Joules/ m 3 Ij'oMr
Steinmett’s Emperical Law for Hysteresis loss: Wh =T]B,ltffi> in watts Where : r| = Steinmetz’ s coefficient in J/m 3. / = frequency in cycles/sec (Hz) Bm- maximum flux density in W b/m 2 v = volume o f the core in m 3
Capacitance o f Parallel Plate Capacitor : A (a) Uniform dielectric medium : C = £0£r — in Farad d Where : A = area o f each plate in m 3 , d - thickness o f dielectric medium in m. s , = relative permitivity o f the medium.
£ (b) Composite dielectric medium : C = ------------------ - ---------- ---------- =r in Farad --------j^ 4-^2 , ^3---------- 1 ----------^ .h o o o -j---- — £rl erl e r) Srn Where : _d_ , d 2 , d ^,... d„ ~ are thickness o f dielectric medium with relative permitivity o f Sri , £, 2 , , ••• Sm respectively.
6 A (c) Dielectric medium partly air : C = - ------ (^) f —------- — in Farad d - t t - —-
Capacitance o f Multiple Plate Capacitor : C ~ {n — l ) -— in Farad d Where : n = number o f parallel plates, A = area o f each plate in m 2 d = separation between two plates in m, £ , = relative permitivity o f medium
Capacitance o f Cylindrical Capacitor : C = in Farad In — n Where : r a , = outside and inside radii resp. in m, I = length o f the cable in m
Capacitance in Series ; Capacitance in Parallel:
= ---- 4 -------- 1 ------ 4-ooo + ----- C. —Ct + C t 4- C-i + 0 0 0 + C c, c, c 2 c 3 c„ 2 Kf = K , + V 2 + V 3 + o o o + K„ V, = K , = K j = o o o K „
Energy Stored in a Capacitor :
w c = - C V 2 = i QV = -^1 i„ Joules C 2 2 2C
Energy Stored per volume o f a dielectric medium : D 2 Wr = ---------- in Joule/m 3 2 £{)£r '
F oree o f Attraction between two plates o f parallel plate capacitor : D 2 e 0e rE 2. 2 F = --------- = ------------ in N/m 2 e 0c r 2
2 C l a s s e s o f E le c t r ic I n s t r u m e n t s
1. Absolute - can indicate the presence o f an electric quantity. No calibration or comparison is necessary, (e.g. tangent galvanometer) 2 Secondary - an instrument in which the value o f electrical quantity to be measured can be determined from the instruments, only when they have been pre-calibrated by comparison with absolute instruments
T y p e s o f S e c o n d a r y I n s t r u m e n t s 1 Indicating instruments - displays the instantaneous values o f electrical quantity on a calibrated scale, (e.g. voltmeter, ammeter, wattmeter etc.) 2 Recording instruments - these give a continuous record o f variations o f an electrical quantity with respect to time. (e.g. load or demand graph, recording wattmeter e tc )
T o r q u e s o n M o v i n g S y s t e m s
1. Deflecting (operating) torque - the force developed in an instrument which moves the moving system o f an instrument in accordance with the magnitude o f the quantity to be measured.
M o v i n g C o i l I n s t r u m e n t It works on the principle o f a o f a dc motor, it has a uniform scale, and a sensitive instrument, sometimes called “ D ’ Arsonval” instrument It is only used for dc measurement.
M o v i n g I r o n I n s t r u m e n t It has no moving coil but which has a moving iron strip or disk it works in the principle o f attraction and repulsion. It can be used both for ac and dc measurements.
D y n a m o m e t e r I n s t r u m e n t These instrument are based on the principle that mechanical force exists between the current carrying conductors. It is essentially consists o f a fixed and moving coil, these coils may be excited separately or they may be connected in series. It can be used both for ac and dc measurements. I n d u c t i o n t y p e I n s t r u m e n t The principle o f operation is similar to that o f induction motor. A rotating magnetic field is set up by the suitably located coils o f the instrument. An aluminum disc is suspended near to the coils in which eddy currents are induced by the rotating flux which tends to rotate the disc. It is only used for ac circuits.
T h e r m o - c o u p l e I n s t r u m e n t These are based on Seebeck effect (thermoelectric effect) The thermo em f is proportional to the difference in temperature between hot and cold junction. These can be used for ac/dc measurement.
H o t w i r e I n s t r u m e n t It is an ac/dc current measuring instrument which is based on the heating effect o f electric current. It consists o f platinum-iridium (it can withstand oxidation at high temperatures) wire which expands when heated which provide deflection o f the pointer.
E le c t r o s t a t i c I n s t r u m e n t The basic principle o f such instrument is that a force o f attraction exists between two or more charged bodies. So these are basically a voltage measuring devices.
15 J t is a cell designed to produce electric current and can be recharged. Secondary cell C. Electrolytic cell B. Chemical cell D. Battery
WH output based on WH input in recharge C. WH output based on AH input in recharge D. AH output based on AH output in recharge
‘Cft. \ i
i. A 120 cm long conductor is carrying a current of 1.2 Amp and is situated at right angles to the field of flux density of 0.65 Tesla. Calculate the force on the conductor. A. 3.264 N C. 1.348 N B, 0.936 N D. 1.587 N
. A core of annealed steel sheet is wound with 1500 turns of wire through which a current of 40 mA is flowing. If the length of the coil is 20 cm, calculate the magnetic strength is Amp-turns per meter. A. 300 C. 400 B. 350 D. 450
). A flat circular coil having 50 loops of wire on it has a diameter of 48 cm. What current must flow in its wires to produce a flux density of 0.005 Tesla at its center? A. 45.5 Amp C. 32.8 Amp B, 38.2 Amp D. 40.5 Amp
2. Permeability in a magnetic circuit corresponds to ______in an electric circuit. A. resistance C. jconductivity B. resistivity D. conductance
A solenoid has a magnetic reluctance of 2.2 x10~3. It has 300 turns and a core area of 5 sq. cm. What is the flux density when the current flowing is 1 Amp? A. 26,300 Gauss C. 34,200 Gauss B. 12,200 Gauss D. 21,200 Gauss
A magnetic circuit consists of silicon steel of 3000 permeability and an air gap. The length of the steel core is 10 cm and the air gap is 2 cm both have the same cross- section of 1.5 sq. cm. A current of V* Amp flows through the windings to produce 2351 Maxwell flux. How many turns are there in the coil? A. 4,120 turns C. 2,500 turns B, 500 turns D. 1,250 turns 'N * , ,
A magnetic circuit consists of silicon steel 3000 permeability of 10 cm length and cross section of 1.5 sq.cm and an air gap of the same cross section and of 2 cm length. A! Amp flows through 500 turns. What is the field intensity at the air gap? A. 250 C. 795 -B. 2,262 D. 1,
Pole strength 160 and 192 are separated by a distance has a force of 19600 dynes. What is the distance in cm? integer choices. A) 1 ' C. 3 B. 2 D. 4
A current of 2 Amp through a coil sets up flux linkages- of 4 Weber-turns. What is the inductance of the coil? A. 8H C ) 2 H B. 0.5 H D. 1 H
a
A. Laplace’slaw C. Fleming’s right hand rule Lenz’s law D. Kirchhoff s voltage law
Amp. The current is cut-off and the flux collapses in 0.01 sec. What is the average voltage that will appear across the coil? A. 20 kV C. 200 V B. 2,000 kV D. 2 kV
is the average voltage induced in the inductor because of this current reversal? A. 100 Volts C. 400 Volts B. ) 200 Volts D. 50 Volts
between the extremities of the wings, when the plane moves horizontally with the speed of 150 miles per hour? The value of the vertical-component of the earth’s magnetic field is 0.65 Gauss at the plane. A; 0.12 Volt. C. 12 Volt B. 0.24 Volt D. 1.2 Volts
energy stored when the steady current is 2 Amp. A. 1.75 mJ C. 17.5 mJ B.: 6.32 mJ D. 63.2 mJ
cm and uniformlywound with twoconductors A and B over one another. A has 90turns and B has 240turns. Calculate the firstprinciple of mutualinductance between the core. A. 10.62 C) 11. B. 10.55 D. 11. 44/When two inductors are connected in series aiding, their total inductance is 40 mH, when connected series opposing the inductance is 17.5 mH. What is the value of mutual inductance? A. 0.5625 C. 56. B) 5.625 D. 562.
of coupling is 41% with mutual inductance opposes the self-inductance. What is the total inductance of the combination? A. 0.94 H C. 1.43 H B. 3.33 H D. 0.49 H
0 n = 0.4 mWb and flux
revprobs.5ept.
process? A. melting C. generating B. magnetic induction D. flow of current
A. JIS C. DIN B, Brown & Sharpe D. VDE
A A.- increase C. does not change B. decrease D. does change
A. do not change C. decrease B. does change D. increase
A. Electrolyticdiffusion C. Electroplating B. Distillation D. Battery manufacture
A. 0.428 C. 0. B. 0.264 D. 0.
resistance of a 200 ft long conductor if the area is 3 x10"5m2. A. 2.5 C. 50 B. 25 D. 12.
diameter. The resistivity is 5.55 x10“® ohm-meter at 20°C. What is the resistance at 20°C? A. 15 ohms. C. 27.5 ohms B. 20 ohms d. 60 ohms
2.956 ft. has a resistance of 207 micro-ohms at 20°C. What is the resistance in ohm per circular mil foot at this temperature of the aluminum bus bar? A, 18.56 C. 14. B. 16.49 D. 19.
Volts. Resistivity of copper is 10.4 ohm-cmil per ft. Calculate the cross sectional area of the coil in circular mil? A. 146 C; 107 B. 168 D. 175
temperature coefficient of resistance at zero degrees centigrade? A. 3.93 x10“3 /°C C. 2.73 x10~3 l°C B. 3.65 x10“3 /°C D.' 4.27 xIO"3 1° C
Figure 5
8 0 2 Q
