Fundmentls of Electricl Circuits Chpter 3 1S. For the circuits shown elow, ) identify the resistors connected in prllel ) Simplify the circuit y replcing prllel connect resistors with equivlent resistor. 5 k 50 ma 6 k 10 k 9 k 18 k ) Resistors in Prllel 9 k 18 k 6 k ) Simplify Req for prllel Resistors = 1/(1/9 1/18 1/6) = 3 5 k 50 ma 10 k 3 k 1U. For the circuits shown elow, ) identify the resistors connected in prllel www.engrcs.com, V1 Fundmentls of Electricl Circuits I pge 30
) Simplify the circuit y replcing ll resistors with equivlent resistor. 5 k 10 k 120 ma 4 k 8 k 9 k 6 k 15 k 2S. Find the equivlent resistnce seen y the source in the following circuit. 200 mv 300 500 600 1. 400 Simplify? Req = (1200 600) 300 400 500 = 1/(1/1200 1/600) 1200 = 1600 200 mv 1600 www.engrcs.com, V1 Fundmentls of Electricl Circuits I pge 31
2U. Find the equivlent resistnce seen y the source in the following circuit. 5 V 1500 6000 1 4 k 2U. Find the equivlent resistnce (R ) in the following circuit with respect to terminls. 12 kω 4 kω 8 kω 4 kω 2 kω 1 kω 2 kω 6 kω 6 kω 500 Ω 12 kω 10 kω 0 Ω 3S. For the following circuit, ) Clculte the nolod voltge vo for the voltgedivider. ) Clculte the power dissipted in R1 nd R2. c) Assuming tht only 1/4 W resistor re ville. The nolod voltge is to e the sme s in (). Specify the smllest vlue of R1 nd R2. I R 1 50 V R 2 500 vo ) find nolod vo? vo = I R 2 www.engrcs.com, V1 Fundmentls of Electricl Circuits I pge 32
vo = (50 / (R 1 R 2 ))*R 2 = (50/(2000500))*500 = 10 V ) Powers? P R1 = R 1 * (50 / (R 1 R 2 )) 2 = 2000 * (50 / 2500) 2 = 0.8 W P R2 = R 2 * (50 / (R 1 R 2 )) 2 = 500 * (50 / 2500) 2 = 0.2 W c) Given: P Mx 1W & vo = 10 V ; Find possile vlue of R 1 & R 2 vo = 10 V vo = (50 / (R 1 R 2 ))* R 2 = R 1 / R 2 = 4 P Mx 1W vo 2 /R 2 1W 10 2 /R 2 ¼ W R 2 400 Ω P Mx 1W vo 2 /R 1 1W 40 2 /R 1 ¼ W R 1 6400 Ω The vlues of R1 & R2 must stisfy 3 rules: R 1 6400 Ω, R 2 400 Ω & R 1 / R 2 = 4 There fore the Minimum vlue R 2 =400 Ω, R 1 = 6400 Ω 3U. For the following circuit, ) Clculte the nolod voltge vo for the voltgedivider. ) Clculte the power dissipted in R1 nd R2. c) Assuming tht only 0.25 W resistor re ville. The nolod voltge (Vo) is to e the sme s in prt (). Specify the vlue of R1 nd R2 tht meets the limittions. I R 1 1 k 250 V R 2 1500 vo Not Provided 4S. Use voltge division or current division to find the specified voltges or currents: ) Suppose the voltge drop cross the 2 resistor in the following circuit A is 40 V, positive t the top of the resistor. Wht is the voltge drop cross the 18 resistor? ) Suppose the current in the resistor in the following circuit A is 60 ma, flowing from left to right. Wht is the current flowing in the 30 resistor? c) Suppose the current in the 1. resistor in the following circuit B is 9 ma, flowing from left to right. Wht is the current in the 30 k resistor? d) Suppose the voltge drop cross the 4 k resistor in the following circuit B is 50 V, Positive t top of the resistor. Wht is the voltge drop cross the 2.4 k resistor? 12 30 1. 2 18 4 k 30 k 60 k 7. 2.4 k (A) (B) www.engrcs.com, V1 Fundmentls of Electricl Circuits I pge 33
) Given V 24 = 40V, Find V 18 30 40V 18 15V V 18 = IR = (40 /(30 18))* 18 = 15 V ) Given I 10 = 60 ma, Find I 30 =? 12 30 30 I 30 I 30 2 V 1 18 Req = 16 V 1 I 10 I 10 Req = 24 (18 30) = 16 V 1 = 16 * 60 = 960 mv I 30 = V1 / ( 30 18) = 960 / 48 = 20 ma c) Given I 1. = 9 ma, Find I 30 =? 1. I 30 k I 1. V 1 4 k 30 k 60 k 7. 2.4 k Req Current Divider Req = (1.2 7.2 2.4 2)= 5 k V1 = (9 ma)(5 k) = 45 V I 30 = V1 / 30 = 45/30 = 1.5 ma d) Given V 30k = 50 V, Find V 2.4 =? www.engrcs.com, V1 Fundmentls of Electricl Circuits I pge 34
1. V 1 =50V 4 k 30 k 60 k V 1 7. 2.4 k V 2 Req = 7.2 2.4 = 1 / (1/7.2 1/2.4) = 1.8 k V2 = (V1/ (1.2 1.8 2))*1.8 = (50/5)*1.8 = 18 V 4U. Use voltge division or current division to find the specified voltges or currents: ) Suppose the voltge drop cross the 40 resistor in the following circuit A is 40 V, positive t the top of the resistor. Wht is the voltge drop cross the resistor? ) Suppose the current in the resistor in the following circuit A is 60 ma, flowing from left to right. Wht is the current flowing in the 30 resistor? c) Suppose the current in the resistor in the following circuit B is 10 ma, flowing from left to right. Wht is the current in the 60 k resistor? d) Suppose the voltge drop cross the 4 k resistor in the following circuit B is 50 V, Positive t top of the resistor. Wht is the voltge drop cross the 2.4 k resistor? 20 30 40 20 4 k 60 k 10 k 7. 2.4 k 2.5 k (A) (B) 5S. The Current in the 9 resistor in the circuit shown elow is 1A. ) Find v g. www.engrcs.com, V1 Fundmentls of Electricl Circuits I pge 35
) Find the power dissipted in the 20 resistor. 20 5 v g 32 40 25 9 1A 2 3 1 ) Vg =? I 9 = 1 A V 9 = 9 * 1 = 9 V Req1 = (12) 9 = 2.25 20 5 I1 v g 32 40 25 V2 V1 2.25 3 I1 = V1/2.25 = 9/2.25 = 4 A V2 = I1 * ( 42.25) = 25 V Req2 = (4 2.25) 25 = 5 Req3 = (20 5) = v g 32 40 V3 5 I2 V2 3 I2 = V2/5 = 25/5 = 5A V3 = I2 * ( 5 3) = 40 V Req4 = ((53) 40) = 6.67 www.engrcs.com, V1 Fundmentls of Electricl Circuits I pge 36
Ig I4 v g 32 V4 6.67 I3 V3 = 40V I3 = V3/6.67 = 40/6.67 = 6 A V4 = I3 * ( 4 6.67) = 6 * 10.67 = 64 V I4 = (V4)/32 = 2 A KCL Ig I4 I3 = 0 Ig = 8 A KVL Vg (10*8) (32*2)= 0 Vg = 144 V ) P 20 =? Using I3 V 4 = 6 * 4 = 24 V which is the sme s V 20 P 20 = (V 20 ) 2 /20 = (24) 2 /20 = 28.8 W 5U. The Current in the 5 resistor in the circuit shown elow is 100 ma. ) Find v s. ) Find the power dissipted in the 40 resistor. 20 5 100 ma v s 32 40 25 9 2 3 1 5U. Find the power delivered y the source (Vs = 10 Volts) in the following circuit. 2 Ω 3 Ω 8 Ω 5 Ω Vs 10 Ω 40 Ω 10 Ω 20 Ω 2 Ω 6 Ω 2.9 Ω 12 Ω 8 Ω www.engrcs.com, V1 Fundmentls of Electricl Circuits I pge 37
6S. ) For the following mmeter circuit, show tht the current in d Arsonvl movement is lwys 1/100 th of the current eing mesured. ) Wht would the frction e if the 100 uv, 10 ua movement were used in 1A mmeter? c) Would you expect uniform scle on d Arsonvl Ammeter? 100 uv, 10 ua i m i mes 10/99 ) Internl Resistnct of d Arsonvl = R DA = 100 uv / 10 ua = so we cn redrw ohmic equivlent: i m i mes 10/99 Apply the current divider i m = i mes (10/99 /(10/99 10)) i m / i mes = 1/100 We ) Rtio = i m / i mes = 10 ua / 1 A = 1/100,000 c) Yes, if d Arsonvl is ssumed to e idel. 6U. ) For the following mmeter circuit, wht is the rtio of current through d Arsonvl movement (i m ) to tthe current eing mesured (i mes ). 50 uv, 1 ua i m i mes ) Wht would the frction e if the 100 uv, 10 ua movement were used in 1A mmeter? c) Would you expect uniform scle on d Arsonvl Ammeter? 1/99 www.engrcs.com, V1 Fundmentls of Electricl Circuits I pge 38
7S. A d Arsonvl voltmeter is shown elow. Find the vlue of Rv for ech of the following full Scle Redings: ) 50 V ) 5 V c) 250 mv d) 25 mv Iv Rv Vv 20 mv 1 ma Voltmeter * We know tht d Arsonvl movement hs Rm = 20 mv / 1mA = 20 * In generl we hve Vv = Iv (Rv 20) Since Mx V is given in the question, we should use I= 1mA which is cuses mximum movement s the Iv ) Vv=50 V 50 =.001(Rv 20) Rv= 49,980 ) Vv=5 V 5 =.001(Rv 20) Rv= 4,980 c) Vv=250 mv.250 =.001(Rv 20) Rv= 230 d) Vv=25 mv.025 =.001(Rv 20) Rv= 5 7U. A d Arsonvl voltmeter is shown elow. Find the vlue of Rv for ech of the following full Scle Redings: ) 100 V )25 V c) 500 mv d) 5 mv Iv Rv Vv 10 mv.2 ma Voltmeter 8S. The ridge circuit shown elow is energized from 6V dc source. The ridge is lnced when R 1 =200,R 2 =500 nd R 3 =800. ) Wht is the vlue R x. ) How much current (in millimperes) does the dc source supply? c) Which resistor in the circuit sors the most power? How much power does it sor? d) Which resistor sors the lest power? How much power does it sor? www.engrcs.com, V1 Fundmentls of Electricl Circuits I pge 39
R1 = 200 R2 = 500 v=6v V1 Io V2 R3 = 800 R x ) Blnced Bridge Io = 0 nd V 1 = V 2 Currents through R1 nd R3 re the sme I1 Current through R2 nd Rx re the sme I2 V = 6 = I1*(200 800) I1 = 6 ma V1 = 800 * 6 ma = 4.8 V = V2 V R1 = V R2 200*I1 = 500*I2 200*6= 500*I2 I2 = 2.4 ma V R3 = V Rx 800*I1 = R x *I2 800*6= R x *2. R x = 2,000 ) I = current of dc source =? I = I1 I2 = 6 2.4 = 8.4 ma c) Which resistor sors most power? P R1 = (200)*(6*10 3 ) 2 = 7.2 mw P R2 = (500)*(2.4*10 3 ) 2 = 2.88 mw P R3 = (800)*(6*10 3 ) 2 = 28.8 mw P Rx = (2000)*(2.4*10 3 ) 2 = 11.5 mw R3 = 800 sors the most power equl to 28.8 mw d) Which resistor sors lest power? R2 = 500 sors the most power equl to 2.88 mw 8U. The ridge circuit shown elow is energized from 10V dc source. The ridge is lnced when R 1 =100,R 2 =200 nd R 3 =1200. ) Wht is the vlue R x. ) How much current (in millimperes) does the dc source supply? c) Which resistor in the circuit sors the most power? How much power does it sor? d) Which resistor sors the lest power? How much power does it sor? www.engrcs.com, V1 Fundmentls of Electricl Circuits I pge 40
R1 =100 R2 = 200 v=10v V1 Io V2 R3 = 1200 R x 9S. ) Find the equivlent resistnce R in the circuit shown elow y using toy trnsformtion involving the resistors R2,, R3 nd R4. ) Repet () using Yto trnsformtion involving resistors R2, R4 nd R5. c) Give two dditionl toy or Yto trnsformtions tht could e used to find R. R1 = 13 R2= R3 = 50 R4 = 40 R5 = 8 R6 = R7 = 7 www.engrcs.com, V1 Fundmentls of Electricl Circuits I pge 41
) toy trnsformtion with R2, R3 nd R4. R1 = 13 A Rct= B R1t R2t R3t Rt = 40 Rt = 50 C R5 = 8 R6 = R7 = 7 RtRct 10 *50 R1t 5 Rt Rt Rct 40 10 50 RtRct 40 *10 R2t 4 Rt Rt Rct 40 10 50 RtRt 40 *50 R3t 20 Rt Rt Rct 40 10 50 New Circuit with Trnsformtion R1 = 13 A R1t = 5 R2t = R3t= 20 B C R5 = 8 R6 = R7 = 7 Req() = 13 5 ((84) (204)) 7 = 33 www.engrcs.com, V1 Fundmentls of Electricl Circuits I pge 42
) Yto trnsformtion with R2, R4 nd R5. R1 = 13 A R1t= Rt R3= 50 R3t = 40 C R7 = 7 R2t = 8 Rct Rt R6 = B R1tR 2t R2tR3t R3tR1t Rt R1t R1tR 2t R2tR3t R3tR1t Rt R2t R1tR 2t R2tR3t R3tR1t Rct R3t New Circuit with Trnsformtion 10*8 8* 40 40 *10 80 10 10*8 8* 40 40 *10 100 8 10 *8 8* 40 40 *10 20 40 Req() = 13 20 ((50 100) (4 80)) 7 = 33 www.engrcs.com, V1 Fundmentls of Electricl Circuits I pge 43
c) Identify t lest couple of trnsforms R1 = 13 R2= R3 = 50 R4 = 40 R7 = 7 R5 = 8 R6 = 9U. ) Find the equivlent resistnce R in the circuit shown elow y using toy trnsformtion involving the resistors R2,, R3 nd R4. ) Repet () using Yto trnsformtion involving resistors R2, R4 nd R5. c) Give two dditionl toy or Yto trnsformtions tht could e used to find R. R1 = 20 R2= R3 = 40 R4 = 400 R7 = 80 R5 = 200 R6 = 100 www.engrcs.com, V1 Fundmentls of Electricl Circuits I pge 44