qLfba7cz

1All: x/113
2Q: 51/60 
3Q1: 7/10 Q2: 8/10 Q3: 9/10 Q4:8/10 Q5: 10/10 Q6: 10/10
4L: 34,5/53
5L2: ?? L3: 7,9/14 L4: 10/14 L5: 6,8/13 L6: 9,8/12
6
71:
81.1 A steady state voltage across two capacitors connected in series: C1 = 10 μF and C2 = 5 μF, is 3 V. What energy is stored in C1 ? 
9(C1*((C2/(C1+C2)*U)^2))/2
10(10*((5/(10+5))*3)^2)/2=5uJ
11
121.2 Suppose a short-circuit were to develop in this electric power system. What should be the reactor inductance, such that at τ=30µs the current rises to i(τ)=20mA. E=100V, Rt=80Ω, Rl=120kΩ. 
13XXXXXXXXXXXXXXXXXXXXXXXX
14
15
161.3 Find the steady state value of the voltage u, after changing position of the switch. E=179V, R=9kΩ, C=8µF.
170,2*E
180,2*179=35,8V
19
20
211.4 A switch openes at t = 0. Calculate increment of the energy stored: ΔW = W∞ − W0 (sign and value with unit). E1 = 17 V; E2 = 17 V, R1 = 1 Ω; R2 = 7 Ω; C = 9 μF.
220(?)uJ
23
24
251.5 An instantenous current entering two capacitors connected in parallel: C1 = 4 μF and C2 = 7 μF, is 8 A. What current flows through C1 at this instant of time? 
26I*(C1/(C1+C2)
278*(4/11)=2,909A
28
29
301.6 A ramp voltage excitation of 9 V/s rise is switched at t = 0 to RC differentiator input: R = 4 kΩ, C = 6 μF. Find the output voltage, at t = 5·T.
31
32XXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
33
341.7 A constant current of 3 mA charges 3 μF capacitor for 5 ms. What energy is stored after this period of time, if the capacitor initial voltage is u(0) = 1 V.
35
36XXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
37
381.8 A switch is closed at t = 0. Calculate the switch current at t = 1 ms. E = 2 V, R = 1 kΩ, C = 1,1 μF.
39Iinf=(E/2)*R - (2/2)*1=1
40I0=2E/3R - (2*2)/(3*1)=4/3
41T=0,5RC - 0,5*1*1,1=0,55
42
43Iinf+(I0-Iinf)*e^(-t/T)
441+(4/3-1)*2,71^(-1/0,55)=1+(⅓)*0,16=1+0,054=1,054mA
45
46
47
481.9 Draw the output waveform of the differentiator shown, in response to the symmetric triangle input of U1 = 7 V magnitude and τ = 5 ms duration. Then, find u2(0.75 τ), sign and value with unit. Assume R = 2 kΩ, C = 2 µF and uC(0) = 0. 
49
50R*C*(U1/(0,5t))
512*2*(7/0,5*5)=4*7/2,5=11,2V
52
53
541.10 A switch opens at t=0. Find the total energy dissipated. R1=2kΩ, R2=7kΩ, C=1µF and E=6,1V. 
55((E*((R1-R2)/(R1+R2)))^2)/2
56((6,1*((2-7)/(2+7))^2)/2=((6,1*((-5/9)^2))/2=(3,38^2)/2=11,48/2=5,7423uJ
57
58
59
602:
61
622.1 A series RLC circuit is connected to 9mA rms current source of adjustable frequency. At ω=1000 rad/s the voltmeter readings are: UR=7V, UL=6V, UC=6V. Calculate indication of the source voltmeter, in V, at ω=2000 rad/s.
63
64SQRT[[((Uc*w1)/w2)-((Ul*w2)/w1)]^2+Ur^2]
65SQRT[[((6*1000)/2000)-((6*2000)/1000)]^2+7^2]=SQRT[(3-12]^2+49]=SQRT[130]=11,40
66
67
68
69
702.2 A sinusoidal waveform u1 of U1=7V rms and f=300Hz is the RC differentiator input: C=6µF, R=|XC|/29. Find the phase shift, sign and value in degrees rounded to the first decimal place, between the output voltage u2 and the input voltage u1: φ=α2−α1.
71
72!!!(?)(?)(?)!!!
73arctan(R) 
741 radian = 57.2957795 deg
75arctan(29)*57.2957795=88,0251
76
77
782.3 Find the phase shift between the source voltage u and its current i, αu-αi in radians, if R=2kΩ, XL=7kΩ, |XC |=4kΩ, u=6√2sin(4000t)V, time in seconds
79
80XXXXXXXXXXXXXXXXXXXXXXXXXX
81=-0,2111
82!!!(?)(?)(?)!!!
83jeśli Xc=Xl to odp to “0”
84
85
862.4 A sinusoidal waveform u1 of U1=6V rms and f=900Hz is the RC integrator input: C=7µF, R=36|XC|. Find the phase shift, sign and value in degrees, between the output voltage u2 and the input voltage u1: ξ=α2−α1.
87
88-arctan(R)
891 radian = 57.2957795 deg
90-arctan(36)*57.2957795=-88,4089
91
922.5 The rms current taken from a voltage source e=21√2sin(7t)V, by a series combination of R=3Ω and L=?, is 1A. Find the inductance, in H.
93
94SQRT[(e/I)^2)-R^2)]/w
95SQRT[(21/1)^2)-3^2)]/7=SQRT[432]/7=20,78/7=2,969
96
97
98
992.6 What resistance R, in Ω, should be connected in series with 3,7mH coil such that at U=230V rms, 50Hz supply, the coil voltage drops to 0,6U ?
100
101Jaką oporność R, w Ω, należy włączyć w szereg z cewką 3,7mH by przy zasilaniu U=230V rms, 50Hz napięcie na cewce spadło do 0,6U ?
102
103Xl=2*3,14*f *L*10^(-3)
104Xl=6,28*50*3,7*0,001=1,1618
105SQRT[((Xl/coeffU)^2)-(Xl*Xl)]=SQRT[((1,16/0,6)^2-1,16^2)]=SQRT[3,75-1,3456]=SQRT[2,4044]=1,55
106
107
1082.7 What reactance of capacitive character |XC|, in Ω, should be connected in series with j900Ω coil such that at U=500V supply, the coil voltage drops to 0,6U.
109
110((1+coeffU)/coeffU)*Xc
111((1+0,6)/(0,6))*900=2400
112
113
1142.8 Find modulus of the given impedance (in Ω), at ω=40000rad/s frequency, if R=28Ω, L=3,0mH, C=10µF. Use of PSpice is recommended.
115
116Zl=w*L*0,001=40 000*3*0,001=120
117Zc=-1/(w*C*0,000001)=-1/0,4=-2,5
118SQRT[(R^2)+(Zl+((Zl*Zc)/(Zl+Zc))^2]
119SQRT[784+(120+[-300/117,5])^2]=SQRT(784+(117,5)^2)=SQRT[14 590,25]=120,738
120
121
1222.9 Find phase of the given impedance (sign and value in deg), at ω=23000rad/s frequency, if R=24Ω, L=2,8mH, C=2µF. Use of PSpice is recommended.
123
124XXXXXXXXXXXXXXXXXXXXXXXXX
125=-53,82
126
127
128
1292.10 Find the coil ammeter indication, in A, if the capacitor rms current is 1A and ωL=5Ω, 1/ωC =9Ω, R=7Ω.
130
131SQRT(Ic^2+((Ic*(1/w*C))/R)^2)
132SQRT(1^2+((1*9)/7)^2)=SQRT(1+(9/7)^2))=SQRT[1+1,653]=SQRT[2,654]=1,628
133
1343:
135
136
1373.1 The voltage across Z(jω)=9Ω +j5Ω load is u=6√2sin(2π 58t)V, f in Hz, t in sec. What energy is dissipated in one period, in mJ?
138
139(Urms)^2*R/(f*(R^2+X^2))*10^3
140(6^2)*9/(58*(81+25))*10^3=324/(58*106)*10^3=324*6148*10^3=0,0527*1000=52,7
141
142
1433.2 A resistive load consumes P*=800W at U=160V rms, f=60Hz supply. Find reactance |XC| of a capacitor that should be connected in series, in Ω, to reduce the power consumption to P=0,7P*, if the combination is supplied by the same voltage.
144SQRT((1-multip)/(multip)) * Urms^2/P*
145SQRT[(1-0,7]/0,7) * 160^2/800=SQRT[0,3/0,7] * 25 600/800=0,6546*32=20,949
146
1473.3 A resistive load consumes 100W at U=190V rms, 60Hz supply. Find a capacitance, in μF, that should be connected in series to maintain the same power consumption, if the combination is supplied from 3U, 50Hz line.
148XXXXXXXXXXXXX
149=3,1174
150
1513.4 The instantaneous power delivered to a capacitor is p=6sin(2ωt)W and its voltage is u=9√2sin(ωt)V, ω=3rad/sec, t in sec. Find the maximum energy stored, in J.
152Pmax/omega
1536/3=2
154
1553.5 What is the maximum power, in W, that can be absorbed by the load impedance, if: R=9Ω, C=10μF, e=8√2sin(ωt)V, ω=500rad/sec, t in sec?
1560.25*(Erms)^2/R
1570,25*8^2/9=0,25*64/9=16/9=1,777
158
159
1603.6 The instantaneous power delivered to a coil is p=14sin(2ωt)W and its voltage is u=3√2sin(ωt+90°)V, ω=8rad/sec, t in sec. Find the maximum energy stored, in J.
161Pmax/omega
16214/8=1,75
163
1643.7 A single-phase motor is supplied with 1600W from 230V, 50Hz line. The motor operates at a pf of 0,5. What is the apparent power, in VA, supplied to the motor?
165P/pf
1661600/0,5=3200
167
1683.8 Find energy, in J, supplied by the source during 8 seconds, if XL=9Ω, |XC|=7Ω, R=5Ω, e=17,8cos900t V.
169((Urms/SQRT(2))^2*R*t)/(R^2+Xl^2)
170([17,8/sqrt(2)]^2*5*8)/(25+81)=12,58^2*40/106=158,42*40/106=6336,8/106=59,78
171
172
1733.9 Find the real power, in W, absorbed by the circuit: u(t)=5sin(200t+45°)V, |XC|=3Ω, XL=4Ω, R=4Ω.
174(Urms/SQRT(2)^2*R)/(R^2+Xl^2)
175([5/sqrt(2)]^2*4)/(16+16)=12,5*4/32=50/32=1,5625
176
177
178
1793.10 The inductive load absorbs 250W of real power at a pf of 0,2 lagging and its voltage is 180V rms. Find the real power absorbed by the transmission line resistance of 5Ω, in W.
180
181(Rline*(RealPower/(Urms*pf))^2)
1825*(250/(180*0,2))^2=5*(250/36)^2=5*6,9444^2=48,22*5=241,1265
183
184
1854:
186
1874.1 Calculate the overall voltage dB gain of this cascaded amplifier circuit, where the output of one voltage amplifier feeds into the input of another. Voltage gains of individual amplifiers are: k1=7V/V, k2=7V/V.
18820*log(k1*k2)
18920*log(7*7)=20log49=20*1,69=33,803
190
1914.2 For the RC circuit, R=2MΩ, C=10µF, sketch the dB gain KdB(ω)=20log[U2(ω)/U1(ω)].
192c. 6dB@0.1rd/s -> -26dB@1rd/s -> -46dB@10rd/s
193
194
1954.3 For the CR circuit shown (high pass filter with speed-up capacitor), find the cut-off frequency fc, in Hz. R2=kR1=4kΩ; k=0,4, C=1,0µF. (Electronic circuit simulator, e.g. PSpice can be applied).
196A=(R/k)^2+2*(R)^2/k - (R)^2=100 000 000 + 80 000 - 16 000 = 164 000 000 
197
198B=(2*PI*(R)^2/k*C)=(2*3,14*4000^2/0,4*1*10^-6=100 530 000/4*10^5=25 132 741*10^-5= 251,132
199
200sqrt(A) /B
201sqrt(164 000 000)/251,132=12 806,24/251,132=50,98
202
203
204
205
206
2074.4 For the assumed 12kHz cut-off frequency, size a noise filtering capacitor, value in nF. Circuit 1 (2) output (input) resistances are: R1=15kΩ, R2=5kΩ.
208(R1+R2)/(2*3,14*R1*R2*f)*1000
209(15+5)/(2*3,14*15*5*12)*1000=20/(6,28*900)*1000=20/5654*1000=0,003538*1000= 3,538
210
2114.5 Find the center frequency, in Hz, of the given band-pass filter: R=3kΩ, C=5µF, L=0,4H, loaded by the Rl=2kΩ resistance.
212(1/SQRT(L*C)/(2*3,14))*1000
213(1/SQRT(0,4*5)/(2*3,14))*1000=((1/sqrt(2))/6,28)*1000=0,7071/6,28*1000=0,11259*1000=112,596
214
215
2164.6 Calculate the capacitor rms voltage at resonant frequency ω=ωr: C=8µF, L=0,12H, R=80Ω, e=6√2sinωt V.
217(e*SQRT(L/C)/R)*1000
218(6*SQRT(0,12/8)/80)*1000=(6*swrt(0,015)/80)*1000=0,009185*1000=9,185
219
220
2214.7 For the given RC circuit: C=9µF, R=7kΩ, loaded by the Rl= 6kΩ resistance, find the gain K(ω) at the cut-off frequency.
222
223XXXXXXXXXXXXXXXXXXXXXXXXX
224
225
2264.8 Find the gain K(ω) = U2(ω)/U1(ω) of the given band-stop filter: R = 5 kΩ, C = 1 µF, L = 5 mH, loaded by the Rl = 6 kΩ resistance, at center frequency.
2270
228
2294.9 Find the resonant frequency fr, in kHz. C=0,9nF; L=0,11mH; R=0,9kΩ. (Electronic circuit simulator, e.g. PSpice can be applied).
230(SQRT((R^2)*C-L)/(2*3,14*R*C*SQRT(L)))/1000
231(SQRT (A) / (B) )/1000
232A=(R^2)*C-L = 900*900*0,9*10^(-9)-0,00011=0,000729-0,00011=0,000619=619*10^6=0,024879
233B=2*3,14*R*C*SQRT(L)=6,28*900*0,9*10^(-9)*sqrt(0,00011)=53,33*10^-9
234
235(SQRT (A) / (B) )/1000=(0,024879/53,33*10^-9)/1000=466 092,044/1000 = 466,341
236
237
2384.10 The parallel RLC circuit: R=9kΩ, XL(ωr)=|XC(ωr)|=7kΩ (ωr is the resonant frequency),is connected to 6,2V rms source of adjustable frequency. Find the phase shift ψ=αi–αiR, sign and value in degrees, at ω=0,9·ωr , where αiR is the initial phase angle of the resistor current and αi is the initial phase angle of the source current.
239
240XXXXXXXXXXXXXXXXXXXXXXXXX
241
2425:
243
2445.1 Find value of R1 resistor, for which there appear only first transmitted and first reflected waves after the switch is closed. Assume lossless transmission line. J=0.5A; Zf=75 Om; R2=35 Om; R3=50 Om.
245R3*(Z0-R2)/(R2+R3-Z0)
246B. 200Om
247
248
2495.2 Calculate current i(inf,⅓ l). Both switches are closing at t=0. Data: E1=10V, E2=5V, R1=25Om, R2=75 Om, Z0=50 Om
250
2510.05A
252
253
254
2555.3 Outline voltage u(t,l/2) of the shorted lossless line after inputting a practical source given by the Norton equivalent: Js=1mA, Gt=1/p=10^(-3)S (where p is characteristic impedance). Other line parameters are: l=10m, C=1nF/m
256B V=0,5; 0-5=0, 5-15=0,5, 15+=0
257
258
2595.4 Current source with Js=0.24A, G=10mS has been connected to the lossless and opened transmission line with the parameters: Cl=1uF/m, Ll=10mH/m, l=5m. What is the value of the voltage at the output of the line for t=ł, where ł is pagation constant?
260
2612*J/(G+sqrt(C/L))
2622*0,24/(0,01+sqrt[1/10000])=0,48/(0,01+0,01)=0,48/0,06=24V
263
2645.5 Indicate the correct voltage observed at x=3l/4, where l is the length of the line and v denotes propagation velocity.
265
266D u= 0,5;0,75, t rises at 1,5 and 2,5
267
268
2695.6 Practical voltage step source, defined by Thevenin's parameters: E0 = 7 V, RIN = 93 Ω, has been connected to input of transmission line, loaded by resistance R2 = 59 Ω. Calculate line current (with unit) at steady state.
270Line characteristic impedance Z0 = 53 Ω.
271
272E/(Rin+R2)
2737/(93+59)=7/152=0,0460526A
274
2755.7 Transmission line characteristic impedance equals Z0 = 84 Ω. Equivalent resistance of source connected to input equals R1 = 68 Ω.
276Calculate value of load resistance, so there exists only first travelling wave in the line.
277Z0 is result
27884Om
279
2805.8 Indicate the correct voltage observed at x=¼, where l is the length of the line and v denotes propagation velocity.
281
282C u=0,5;0,75, t rises at 0,5; 3,5
283
284
2855.9 Outline voltage u(t, 1/2 l) of the opened lossless line, after inputting practical source, given by the Thevenin's equivalent: E0 = 1 V, R0 = Z0 = 100 Ω. Line propagation time equals 1 µs.
286
287B u=½;1, t rises at 5*10^-7; 1,5*10^-6
288
289
2905.10 Practical voltage step source, defined by Thevenin's parameters: E0 = 10 V, RIN= 96 Ω, has been connected to input of transmission line, loaded by resistance R2 = 53 Ω. Calculate load voltage at steady state.
291Line characteristic impedance Z0 = 51 Ω.
292
293E*R2/(Rin+R2)
29410*53/(96+53)=530/149=3,557V
295
2966:
297
2986.1 Find the input impedance of a given lossless line. Its parameters are: L1=10mH/m, C1=1uF/m,1=a/4=10m and the load impedance id Z2(jw)=400 Om (a - length of the wave within the lane)
29925 Om
300
3016.2 Find the input impedance of a given lossless line. Its parameters are: L1=1mH/m, C1=10uF/m,1=a/4=40m and the load impedance id Z2(jw)=20 Om (a - length of the wave within the lane)
3025 Om
303
3046.3 Calculate modulus of the input impedance of a lossless line, loaded by capacitive impedance, |Xc| = 200 Ω.
305Line parameters are: L = 10 mH/m, C = 1 µF/m, l = λ/4 = 10 m.
30650 Om
307
3086.4 Select proper standing wave of current in a 3/4-wave shorted line, if the input voltage is u(t) = 20 sin(314 t) V.
309a.A looks like 1,5 hills, 3a/4; a/4
310
311
3126.5 Sketch the voltage standing wave of a quarter-wave opened line of the input voltage is u0=20sqrt(2)sin(314t)[V]
313B horizontal arrow to the left, graph rising to the right
314
315
3166.6 Calculate modulus of the input impedance of a lossless line loaded by impedance Z(jw)=10+j10 Om. Line parameters are: L=10mH/m, C=uF/m, l=a/2=10m.
31714.14 Om
318
3196.7 Find input impedance of a lossless transmission line supplied with a sinusoidal signal with wave length a=4*l loaded with the resistor R=100 Om (l=10m = line length, p = 50 Om - line impedance).
32025 Om
321
3226.8 Find the rms voltage at the input, of a half- wave opened line, if the input voltage is u0(t)=20sqrt(2)sin(314t)V.
32320V
324
3256.9Sketch the voltage standing wave of a quarter- wave shorted line if the input voltage is u0(t)=Usqrt(2)sin(314t)V (y - the distance from the line).
326B arrow to the left, graph going down at 0
327
328
3296.10 Find input impedance of a lossless transmission line supplied with a sinusoidal signal with wave lenth a=4*l loaded with the resistor R=25 Om (l=12m - line length, p=50 Om - line impedance)
330100 Om
331
332LABS
333
334Lab 3:
3353.1 Calculate the initial condition uc(0-) for C1=8,6μF. Data: E=8,3V, Rgen = 95Ω, R1=1723Ω. The unit must be placed.
336E
3378.3V
338
3393.2 Calculate iC1(0+) in milliamps. Data: E=8,3V, Rgen = 95Ω, R1=1723Ω, C1=8,6μF. The unit must be placed.
340E/R1*1000
3418,3/1723*1000=4,816mA
342
3433.3 Calculate uR1(0+). Data: E=8,3V, Rgen = 95Ω, R1=1723Ω, C1=8,6μF. The unit must be placed.
344-E
345-8,3
346
3473.4 Calculate time constant T in milliseconds. Data: E=8,3V, Rgen = 95Ω, R1=1723Ω, C1=8,6μF. The unit must be placed.
348XXXXXXXXXXXXXXXXXXXXXXXX
349
3503.5 Calculate the energy stored in the capacitor for t=0. Data: E=8,3V, Rgen = 95Ω, R1=1723Ω, C1=391μF. The result should be in uJ.
351XXXXXXXXXXXXXXXXXXXXXX
352
3533.6 Determine initial condition iL1(0-) for coil L1=97. Data: E=8,3V, Rgen=95Ω, R1=1723Ω. The unit must be placed.
354E/Rgen*1000
3558,3/95*1000=87,368mS
356
357
3583.7 Calculate iR1(0+) on R1. Data: E=8,3V, Rgen=95Ω, R1=1723Ω, L1=97mH. The unit must be placed.
359XXXXXXXXXXXXXXXXXXXXXX
360
3613.8 Determine the voltage value uL(0+). Data: E=5,9V, Rgen=119Ω, R1=1454Ω, L1=67mH. The unit must be placed.
362E*R1/Rgen
3635,9*1454/119=72,089V
364
3653.9 Determine the time constant T in microseconds (us). Data: E=21,8V, Rgen=175Ω, R1=1692Ω, L1=132mH. The unit must be placed.
366L/R1
367132/1692=0,078
368
3693.10 Calculate energy stored in a coil for t=0+ . Data: E=21,4V, Rgen=102Ω, R1=1654Ω, L1=142mH. The value should be in mJ. 
370XXXXXXXXXXXXXXXXXXXX
371
3723.11 Calculate the initial condition uc(0-) for a C1=15,7μF. Data: E=17,6V, Rgen = 107Ω, R1=1025Ω. The unit should be placed.
373E*R1/(R1+Rgen)
37417,6*1025/(1025+107)=18040/1132=15,936V
375
3763.12 Calculate the initial condition iL1(0-) for a coil L1=97. Data: E=8,3V, Rgen=95Ω, R1=1723Ω. The unit must be placed.
377E/Rgen*1000
3788,3/95*1000=87,368mA
379
3803.13 Determine the uL(0+) on L1=97mH after opening the key. Data: E=8,3V, Rgen=95Ω, R1=1723Ω. The unit must be placed.
381-E*(R1/Rgen)
382-8,3*(1723/95)=-150,535V
383
3843.14 Calculate current ic1(0+) flowing through capacitor C1 = 8,6 μF. Data: E = 8,3 V, Rgen = 95 Ω, R1 = 1723 Ω. The unit must be placed.
385XXXXXXXXXXXXXXXXXXXX
386
387
388Lab 4:
389
3904.1 Determine value of resistance R1 (in Ω) that the current flowing in the circuit is critically suppressed. Data: E=13,0V, Rgen=424Ω, C1=19,7nF, L1=94mH. The unit must not be placed.
391(2*sqrt(L1/C1)*1000)-Rgen
392(2*sqrt(94/19,7)*1000)-424=2*sqrt(4,771)*1000-424=4368,78-424=3944,786
393
394
3954.2 On the oscilloscope, the voltage waveform in the second order circuit was observed. What kind of a response was registered?
396Response weakly suppressed
397
398
3994.3 Calculate i(0+) value for the circuit below. Data: E=1,7V, Rgen=465Ω, R1=9,79Ω, R2=1041Ω, R=4,0Ω, C1=4,5μF, L2=242mH. The unit should be in mA.
400
401XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
402
403
4044.4 Calculate the current i(∞) value. Data: E=1,8V, Rgen=226Ω, R1=2,72Ω, R2=1205Ω, R=5,3Ω, C1=6,8μF, L2=86mH. The unit should be in mA.
405E/(R2+R+Rgen)*1000
4061,8/(1205+5,3+226)*1000=0,00125322*1000=1,253mA
407
408
4094.5 Calculate u(0+) for the circuit given below. Data: E=14,3V, Rgen=160Ω, R1=1139Ω, R2=1103Ω, R=1459Ω, C1=2,1μF, L2=140mH. The unit must be placed.
410(E*R1)/(R1+R+Rgen)
411(14,3*1139)/(1139+1459+160)=16 287,7/2758=5,905V
412
413
4144.6 Calculate u(∞) in a steady state of the circuit given below. Data: E=14,0V, Rgen=71Ω, R1=504Ω, R2=252Ω, R=1152Ω, C1=5,2μF, L2=196mH. The unit must be placed.
415(E*R2)/(R2+R+Rgen)
416(14*252)/(252+1152+71)=3528/1475=2,391V
417
4184.7 Voltage U=1,6+j8,9 [V] need to be converted to form: U=|U|ejφ. Calculate |U|. The unit must be placed.
419sqrt(A^2+B^2)
420sqrt(1,6^2+8,9^2)=sqrt(2,56+72,21)=9,042V
421
4224.8 Voltage U=4,3+j3,6 [V] need to be converted to the form: U=|U|ejφ. Calculate phase φ in degrees. The unit must not be placed.
423XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
424
4254.9 Voltage U=4,3+j3,6 [V] need to be converted to the time domain: u(t)=UAsin(ωt+φ). Calculate the amplitude value UA . The unit must be placed.
426sqrt(A^2+B^2)*sqrt(2)
427sqrt(4,3^2+3,6^2)*sqrt(2)=sqrt(31,45)*sqrt(2)=5,608*sqrt(2)=7,93V
428
4294.10 Calculate a module of the voltage for symbolic form: U=|U|ejφ if in time domain the signal is: u(t)=3,9sin(366t+58°) [V]. The unit must be placed.
430Umax/sqrt(2)
4313,9/sqrt(2)=2,757V
432
4334.11 Calculate the time period T of the sinusoidal waveform: u(t)=6,1sin(619t+139º) [V].The unit should be placed.
4342*3,14/w*1000
4356,28/619*1000=10,14ms
436
4374.12 The current i(t)=60sin(2π457t+86°) mA flows through the C=5,3μF .Calculate the voltage drop across the capacitor C as measured by the effective value voltmeter. The unit must be placed.
438Imax/(2*pi*w*C*sqrt(2))*1000
43960/(457*5,3*sqrt(2))*1000=60/21 522,2135*1000=0,00272*1000=2,782V
440
441
4424.13 The current i(t)=60sin(2π457t+86°) mA flows through L=8,8mH. Calculate the voltage drop across the coil L as measured by the effective value voltmeter. The unit must be placed.
443XXXXXXXXXXXXXXXXXXXXXXXXXXXXX
444
445
446
4474.14 Determine a phase shift (in degrees) between CH1(Kanal 1) and CH2(Kanal 2) of the oscilloscope. If the waveform on channel 2 is ahead of the signal on channel 1, enter the result with a "-". The time base on the oscilloscope is equal 2μs.
448XXXXXXXXXXXXXXXXXXXXXXXXXXXXX
449
450Lab 5: 
451
4525.1 The RC circuit contains R=1,9kΩ i C=1,9μF and creates low-pass filter. Calculate the border frequency of this system in kHz.
453XXXXXXXXXXXXXXXXXXXXXXXXXXXXX
454
4555.2 The low-pass filter contains: R=7,1kΩ i L=206mH. Calculate the boundary pulsation of this system in rd/s.
456XXXXXXXXXXXXXXXXXXXXXXXXXXXXX
457
458
459
4605.3 Match the question to answer. The question is about the perfect series resonance.
461
462The current flowing through the series connected elements L and C for the resonant 
463frequency. 
464The current can have any value
465
466A series resonance is a 
467resonance of Voltage
468
469Voltage on both elements connected in series L and C for the resonant frequency
470The voltage is always zero
471
4725.4 Match the question to answer. The question is about an ideal parallel resonance.
473
474The total current flowing through both parallel connected elements L and C for the resonant frequency.
475The current is always zero
476Voltage on both elements connected in parallel L and C for the resonant frequency
477The voltage can take any non-zero value
478
479
480Parallel resonance is a resonance of
481currents
482
4835.5 The impedance of the resonant system is: Z(ω)=j[(9506-0,08ω2)/(2242-3,8ω)]. Calculate the serial resonance frequency in Hz.
484Z(ω)=j[(A-Bω2)/(C-Dω)]
485(1/(2*PI))*SQRT(A/B)
486(1/(2*PI))*SQRT(9506/-0,08)=1/(6,28)*sqrt(118 825)=0,15923*344,71=54,862 [Hz?]
487
4885.6 The impedance of the resonant system is: Z(ω)=j[(9413-0,26ω2)/(1289-6,4ω)]. Calculate the parallel resonance frequency in Hz.
489Z(ω)=j[(A-Bω2)/(C-Dω)]
4901/(2*PI)*C/D
4911/(6,28)*9413/0,26=0,15923*201,406=32,054 [Hz?]
492
4935.7 The impedance of the resonant system is: Z(ω)=[1289+0,26ω]+j[(9413-6,4ω)]. Calculate the resonant frequency in rd/s.
494Z(ω)=j[(A-Bω2)/(C-Dω)]
495C/D
4961470,78125
4975.8 Calculate the quality factor of the serial RLC. Data: R=32Ω, L=99mH, C=9,3nF.
498
499XXXXXXXXXXXXXXXXXXXXXXXXXXXXX
500
501
5025.9 Calculate the quality factor of the parallel RLC. Data: R=49kΩ, L=47mH, C=3,9nF.
503R*sqrt(C/L)
50449*sqrt(3,9/47)=3,9*sqrt(0,050649)=49*0,22505=14,1149
505
506
5075.10 Choose the correct frequency characteristic
508
509XXXXXXXXXXXXXXXXXXXXXXXXXXXXX
510
511
5125.11 Derive the formula for the resonant frequency of the circuit
513d (1/2pi)*sqrt[(1/(LC)-(1/(RC))^2)]
514
5155.12 Calculate the A1 ammeter indication. Calculate the value in A unit (do not write the unit in the answer box)
516
517XXXXXXXXXXXXXXXXXXXXXXXXXXXXX
518
519
5205.13 Calculate the power received from the sinusoidal current source. (Place the answer in W unit)
521
522XXXXXXXXXXXXXXXXXXXXXXXXXXXXX
523
524
525
526
527Lab 6:
5286.1 Transmission line with: RL=500 mΩ/m, GL=2 μS/m, LL=2,5 μH/m, CL=100 pF/m, length l=700 m. What is the characteristic impedance of the line, in Ω ?
529w=f/(2*pi)=60/(2*PI)=9,55
530sqrt((Rl-w*Ll)/(Gl-w*Cl))
531=500.107 Om
532
5336.2 Transmission line with a length of 10m has a characteristic impedance Zf=76Ω. Calculate the current value in a steady state i(0,∞), Data: E=9,7V, R1=32Ω, R0=122Ω. The unit must be placed.
534I = E/(R1+R0)
5359,7V/154Om = 0.0629 A
536
5376.3 Transmission line with a length of 10m has a characteristic impedance Zf=93Ω. Calculate a steady state voltage u(0,∞). Data: E=1,2V, R1=45Ω, R0=83Ω. The unit must be placed
538XXXXXXXXXXXXXXXXXXXXX
539
5406.4 Transmission line with a length of 10m has a characteristic impedance Zf=93Ω. Calculate voltage u(0,0+), that is, the voltage appearing at the entrance of the line after the key is turned on. Data: E=1,2V, R1=45Ω, R0=83Ω. The unit must be placed.
541XXXXXXXXXXXXXXXXXXXXX
542
5436.5 Transmission line with: RL=500 mΩ/m, GL=2 μS/m, LL=2,5 μH/m, CL=10 pF/m, length l=700 m. Write a correct answers:
544if sqrt(R*G) > 0 → lossy else → not lossy
545if R/L == G/C → non deforming else → deforming
546
5476.6 Transmission line with a length of 10m has a characteristic impedance Zf=76Ω. Calculate the reflection coefficient from the line output. Data: E=9,7V, R1=32Ω, R0=122Ω.
548N = (Zf - R0) / (Zf + R0)
549(76-122)/(76+122) = -0.2323
550
5516.7 Transmission line with: RL=5,8 Ω/m, GL=9,3 S/m, LL=13 μH/m, CL=13 pF/m. What is the speed of wave propagation in a line of length l=3,6 m in km/s?
5521/sqrt(Ll*Cl)*10^5
5531/sqrt[13*13]*10^5=1/sqrt[169]*10^5=1/13*10^5=0,076923,07692*10^5=76923,07692
554
5556.8 Transmission line with a length of 10m has a characteristic impedance Zf=93Ω. Calculate the current i(0,0+), the current appearing at the entrance of the line after the key is turned on. Data: E=1,2V, R1=45Ω, R0=83Ω. The unit must be placed.
556E/(R1+Zf)
5571,2/(45+93)=1,2/138=0,008695
558
5596.9 Transmission line with a length 10m has a characteristic impedance Zf=97Ω. Calculate the reflection coefficient from the line entry. Data: E=5,3V, R1=65Ω, R0=100Ω.
560(Zf-R1)/(Zf+R1)
561(97-65)/(97+65)=32/162=0,1975
562
5636.10 A sinusoidal wave of a period 66 ns was given to a transmission line with a length 9 m. Calculate the ratio of the wavelength to the length of the transmission line. Assume wave velocity in the line equal wave velocity in the vacuum.
564t*v/l
56566*10^(-9)*299792458/9=7,33*299792458*10^(-9)=2,1984
566
5676.11 Transmission line with: RL=4,3 Ω/m, GL=2,8 S/m, LL=13 μH/m, CL=15 pF/m. What is the time of crossing a line of length l=5,6 m. Give the result in ns.
568l*sqrt(Ll*Cl)
5695,6*sqrt[13*15]=5,6*sqrt[195]=5,6*13,96424=78,199
570
5716.12 Transmission line with: RL=0 Ω/m, GL=0 S/m, LL=13 μH/m, CL=15 pF/m. What is the characteristic impedance of a line of length l=5,6 m. Give the result in Ω without a unit.
572SQRT(Ll/Cl)
573sqrt[13*10^(-6)/15*10^(-12)]=sqrt[0,86666*10^6]=sqrt[866 666,66]=930,949 Om
574
575
576
577
578
579
580
581
582
583
584
585
586From term 0
587
5880.1 (Lab 5.8) Calculate the quality factor of the serial RLC. Data R = 23Ω, L = 79mH, C = 9,0nF
589
590Q = (1/R)*(sqrt(L/C)
591Q = (1/23)*(sqrt(79/9) = 0.128
592
5930.2 Find the total energy stored at the steady state condition in µJ.
594
595I = (4/5)J
596Uc = 1/5 * R * I
597W = (C*Uc^2 - L*I^2)/2
598
5990.3 (Q 1.8) A switch is closed at t = 0. Calculate the switch current at t = 1ms.
600
601I1 = E/2R
602I0 = 2E/3R
603T = 0,5RC
604i(t) = I1 + (I0 - I1)*e^(-t/T)
605
6060.4 (Lab 6.12) Transmission line with Rl = 0Ω/m, Gl = 0 S/m Ll = 23 µHm, Cl = 15pF/m. What is the characteristic impedance of a line of length l = 2,2m. Give the result in Ω without a unit. 
607
608Z = sqrt(Ll/Cl)
609
6100.5 (Lab 5.1) The RC circuit contains R=7,1kΩ i C=5,2μF and creates low-pass filter. Calculate the border frequency of this system in kHz.
611
612w = 1/(RC) 
613
6140.6 (Lab 5.13) Calculate the power received from the sinusoidal current source (Place the answer in W unit).
615
616????
617
6180.7 (Lab 5.12) Calculate the A1 ammeter indication. Calculate the value in A unit(do not write the unit in the answer box)
619
620????
621
6220.8 (Lab 3.13) Determine the Ul(0+) on L1 = 133mH after opening the key. Data E = 19,5V ; Rgen = 487Ω, R1 = 1723Ω. The unit must be placed.
623
624????
625
626
6270.9 (Lab 6.4) Transmission line with a length of 10m has a characteristic impedance Zf = 57Ω. Calculate voltage U(0,0+), that is, the voltage appearing at the entrance of the line after the key is turned on. Data E = 6,6V ; R1 = 37Ω ; R0 = 145Ω. The unit must be placed. 
628
629????
630
6310.10 (Q 4.8) Find the gain K(ω) = U2(ω)/U1(ω) of the given band-stop filter: R = 1 kΩ, C = 8 µF, L = 3 mH, loaded by the Rl = 5 kΩ resistance, at center frequency.
6320
633K(ω) = ((Rl/(R+Rl)/sqrt(2)) ????
634
6350.11 Calculate the power received from the sinusoidal source: i(t) = 2sqrt(2)*sin(314+60°)mA
636
6370.12 Calculate voltage u(infinity) for steady state in the circuit 
638
6390.13 (Q 5.1) Find value of the R1 resistor, for which there appear only first transmitted and first reflected waves after the switch is closed. Assume lossless transmission line
640
641200Ω
642
6430.14 (Q 4.6) Calculate the capacitor rms voltage at resonant frequency(w = wr): C = 4µF, L = 0,08H, R = 40Ω, e = 3sqrt(2)sinwt.
644
645(e*sqrt(L/C))/R // !!! e divide by sqrt(2) -> in this case e = 3 !!!
646((3*sqrt(0,08/4))/40 = 10.6V
647
6480.15 Practical voltage source, defined by Thevenin’s parameters. Calculate line current
649
650E/(Rin+R2)