AC Circuits Questions and Answers

C A transformer has a primary i What sort of transformer is it il Calculate the turn ratio 1 mark 1 mark it If the primary coll is connected to the 240v 1 mark v Calculate the efficiency of the transformer if the primary current is 0 6A and

C A resistance of 15 Q is connected in series with an inductance of 0 25 hen across 220v 50Hz ac supply calculate the D ii iv V vi VII total impedance 1 mark current through the circuit 1 mark voltage across the resistance and inductance 1 mark Power factor 1 marks 1 marks 2 marks Phase angle active and apparent power time equation for voltage and current time equation for current 1marks 1marks

Which of the following figures give the correct variation of the magnitude of output voltage as a function of the frequency v does not change with frequency NCERT Vt a b t c V L d

Three impedances are connected in series and energized by a 1 phase ac supply The impedances comprise of i a resistance of 50 and inductance of 25 mH i a resistance of 50 and capacitance of 500uF ii a resistance of 50 and capacitance of 600uF If the supply voltage v t 260 sin 377t 45 calculate 1 circuit impedance 1 power factor ii current iv voltage across each impedance v active power supplied by the source

3 0 5 m s 4 50 m s In an LCR series ac circuit the voltage across each of the components L C and R is 60V then the voltage across the LC combination is 2 60 2 V 4 30 V 1 Zero 3 120 V Block A and B is co

mpedance is a measure of the opposition to the flow of alternating electrical current It consists of two parts called resistance and reactance Impedance Z in ohms 2 can be expressed as a complex number where the real art represents resistance and the imaginary part represents reactance In the series circuit shown the total impedance is the sum of the individual impedances Assuming that the light bulbs are pure resistive and the motors re pure reactive find the total impedance in this circuit and express it in the form Z a bi CID ve 4 50 52 20 2

Part II QUANTITATIVE PROBLEMS 30 points each MUST show your work to receive credit A correct final answer without steps is not acceptable and will result in no credit Partial credit may be given 4 In an R L C series circuit R 300 2 L 0 400 H and C 6 00 108 F When the ac source operates at the resonance frequency of the circuit the current amplitude is 0 500 A a What is the voltage amplitude of the source b What is the amplitude of the voltage across the resistor across the inductor and across the capacitor c What is the average power supplied by the source d What is the power factor of the circuit if the ac source operates at 1 2 times of the resonance frequency

4 In an R L C series circuit R 300 Q2 L 0 400 H and C 6 00 10 operates at the resonance frequency of the circuit the current amplitude is 0 500 A a What is the voltage amplitude of the source b What is the amplitude of the voltage across the resistor across the inductor and across the capacitor c What is the average power supplied by the source d What is the power factor of the circuit if the ac source operates at 1 2 times of the resonance frequency R 300 XL Vr 150 volts b v IX S WL Vmax V 20x100 2 4 VC V 20x10 2 4 c xc 5 x 10 4 x 4 24 x Imax XL Xc W VLC I 5A I IR V 5 x 300 V 150 volts 1290 994 volts 1290 994 volts W LC W 08 2 Vmax Imax LX 6 104 2 4 130 X 5 2 37 90 w W

2 A series RLC circuit has a peak current of 1 6 A with a frequency of 6 0 kHz If the resistance of the circuit is 18 kn the capacitance of the circuit is 20 F and the inductance of the circuit is 26 H determine the average power of the circuit over one cycle A 36 000 W B 23 000 W C 29 000 W D 90 000W

A 115 F capacitor whose initial charge is 3 91 x 10 coulomb is placed in series with a 2000 2 resistor and a switch as shown When the switch is closed the capacitor begins to discharge a What is the time constant for the circuit in seconds b What is the current through the circuit when t 2 0RC and when t 4 0RC 115 F 2000 2

In the study of alternating electric current instantaneous voltage is modeled by the equation e Emax sin 2aft where f is the number of cycles per second Emax is the maximum voltage and t is the time in seconds Find the smallest posit value of t if Emax 11 e 8 and f 80 Determine the smallest positive value of t ta Round to 5 decimal places

a Old incandescent lightbulbs have a purely resistive metal filament through which flows an alternating current If an incandescent bulb uses an average power of 75 0 W when connected to a 60 0 Hz power source having a maximum voltage of 170 V what is its resistance in Q Q b Another incandescent bulb with an average power usage of 100 W is connected to the same AC power source with the same frequency and maximum voltage What is its resistance in Q

3 A three phase three wire ABC system with an effective line voltage of 106 1 V has a balanced connected load with impedances of Z 15L 30 Q Obtain the line and phase currents by the single line equivalent method 4 A star connected load consists of three identical coils each of resistance 30 and inductance 127 3 mH If the line current is 5 08 A calculate the line voltage if the supply frequency is 50 Hz

Consider the circuit in Eigure 1 Assume that L 200 0 mH Figure S ww R 60 0 V R eeee L 1 of 1 125 50 Submit Part D 115 00 Submit Part E After the switch has been closed a long time what is the current through the resistor R 15 0 Express your answer in amperes 115 00 VAX 3 Submit Request Answer VAXO Request Answer Return to Assignment VAE After S has been closed a long time it is opened again Just after it is opened what is the current through the R 15 0 2 resistor Express your answer in amperes Request Answer 3 C A A A Review

Consider the circuit in Figure 1 Assume that L 200 0 mH Figure S R 60 0 V R Meele L 1 of 1 Part A Just after the switch is closed what is the current through the resistor R 15 02 Express your answer in amperes Ison Submit Part B 125 50 Submit Just after the switch is closed what is the current through the resistor R 25 5 Express your answer in amperes VAZO Part C VAE Request Answer 125 50 Request Answer A A After the switch has been closed a long time what is the current through the resistor R 25 5 2 Express your answer in amperes VAZO F

35 5 V battery with negligible internal resistance 55 02 resistor and a 1 45 mH inductor with egligible resistance are all connected in series with an open switch The switch is suddenly closed Part A How long after closing the switch will the current through the inductor reach one half of its maximum value Express your answer in microseconds t 18 3 us Submit Correct Correct answer is shown Your answer 18 2 us was either rounded differently or used a different number of significant figures than required for this part Part B Previous Answers How long after closing the switch will the energy stored in the inductor reach one half of its maximum value Express your answer in microseconds t VAX ps

AC voltage V t 20 sin 2t of frequency 50 Hz is applied to a parallel plate capacitor The separation on between the plates is 2 mm and the area is 1 m The amplitude of the oscillating displacement current for thong mather applied AC voltage is Take 8 85 x 10 F m mathongs mathongo mathonge mathango mathongo 1 21 14 Amathongo 2 83 37 A 3 27 79 A ang mathango mathongemathongo mathongo mathon 455 58 mathangamothongo mothongo mathongo mathon

56 Two solenoids of equal number of turns have their lengths and the radii in the same ratio 1 2 The ratio of their self inductances will be Kerala CEE 2011 a 1 2 b 2 1 c 1 1 d 1 4 e 1 3

Q5 22 July 2021 Shift 1 mathongemathonge mathango Arathongo In a circuit consisting of a capacitance and a generator with alternating emf Eg Eg sin wt Vc and I are the voltage and current Correct phasor diagram for such circuit is mathongs mathongo Pathong Eg cc vc 6 H thong Ic othongo 2 mathongo moth mathongo mvegek mathongo mathongthongo Ic 1 mathonge mathongo matho mathogo mathango mathongo otthongo mathongo mathongo no mathongo mathonga mahonnomathongs mathongs mathongo mothongo cot mathongo mathango mathonga mathongo mathongo mothongo mathongo mathongo mathango mathongo mothonge mathongo mathongo mathongo mathongo mathongo mathe mathango mathongo mathooo Ichongo mathango mathonge mathongo mothongo mathonge mathongo mathongo mathongo mathango mathango mathongo mathongo mathongo mathongs mathongomathango mathongo mathongo mathongo mathange mathongo mathongo mothongo mathangamathongo MathBoleTohMathonGo www mathongo com mathongo mathongo mathongo mothongo 3 10

Q2 20 July 2021 Shift 1 In an LCR series circuit an inductor 30mH and a resistor 1n are connected to an AC source of angular 3 frequency 300rad s The value of capacitance for which the current leads the voltage by 45 is 10 F Then the value of x is

38 Ac CCIO Sv Find the PD across R 38 Find the impedance of the given circuit for 1702 2002 www For 20 F HH Ans 4 V w i direct current ii alternating current of frequency Ich 10 kHz Ans i infinite ii 32 2

8 An LR circuit consists of R 40 2 and inductance of 3 H An AC voltage 200 V and frequency 10T 50 Hz is applied to the circuit The current in the circuit is approximately equal to Xc 1 4 A 40 Q mmmm 3 10T H 200 V 50 Hz 2 1 A

38 Ac v Find the PD across R 38 Find the impedance of the given circuit for Timang och 2002 Far 20 F wwth Ans 4 V Apar no w i direct current ii alternating current of frequency Ich 10 kHz Ans i infinite ii 32 2 356

A copper disc of diameter 36 cm rotates with its plane at right angles to a uniform magnetic field of induction 20 Wb m at the e m f induced between two points one at the edge of the disc and the other at the S of 250 r p m Find

An alternating e m f of peak value 110V and frequency 50 hz is connected across LCR series circuit with R 1000 L 10mH and C 25 uF Calculate the inductive reactance capacitive reactance and impedance of the circuit

Ans 0 55 H 32 A coil has a current of 1 0 A and a power of 100 W from an AC source of 110 V and 50 Hz Find the resistance and the inductance of the coil Ft Hint P 1 R Ans 100 2 0 146 H

40 cm and the size of image is twice as that of object then the object distance is 2 20 cm 4 30 cm 1 60 cm 3 40 cm 110 2 87 The reading of the A C voltmeter in the Q 87 fra network shown in figure is where V is in volt 1 400 V 3 200 V 1102 ww X 200 00000 X 200 V 220 2 sinest for any a 2 220 V 4 Zero B 1 60 cm 3 40 cm V 11023 1 400 V 3 200 V 110 ww 2 20 cm 4 30 cm A C de X 200 00000 X 2002 V 220 2 sinel die 2 220 V 4 kams

Hint P I R Ans 100 2 0 146 H 33 A sinusoidal voltage V 200 sin 314 t is applied to a resistor Find i rms voltage ii rms current and iii power dissipated as heat 10 Ans 1 200 2 ii 20 2 iii 2000 W

An inductor x 292 a capacitor xc 892 and a resistance 892 is connected in series with an A C source The voltage output of A C source is given by v 10 cos 100nt If the instantaneous potential 4x difference between A and B is when it is half of the voltage output from source at that instant than what 7 is the value of x X 202 X Amm 8 02 B 8 52

The graph shows current v s voltage in a series RLC A C circuit The arrow indicates the direction that this curve is drawn as tim progresses In this plot the O O current lags the voltage by about 90 degrees current leads the voltage by about 90 degrees O current and voltage are in phase voltage current

50 A resistor R 300 Q and a capacitor C 25 f are connected in series with a 50 V Hz T AC source The average power dissipated in the circuit is Options 1 2 3 0 5 W 1 0 W 2 0 W 1 5 W

1 Induction furnace 3 Speedometer of automobile The power consumed in the circuit is 1 1 kW 3 3 kW 4 Crystallography 2 2 kW 4 4 kW R 100 L 1 10m www dr C V 200 V 50 Hz H 1 mF

what does source mean Choose the incorrect statement s 1 Dimensional formula of impedance is ML T A 2 Quality factor of a circuit for an AC source is unitless 3 Phase difference between current and the source is independent of the frequency of the source 4 For an LC circuit in parallel the currents through L and C are 180 out of phase with each other

For the given circuit current through the inductor is 0 9 ampere while the current through the capacitor is 0 6 ampere and current through the resistor is 0 4 ampere The current through source of emf is wwww V V6 sin of O 0 9A O 0 5A 03A O 0 7A

4 An inductor L 8 45 mH a capacitor C 250 F and a resistor R 10 0 2 are connected in series to ar ac voltage source with a peak voltage of 120 V and operated at the resonant frequency initially a Calculate the resonant frequency fin Hz b Calculate the impedance of the circuit and the phase angle at resonance The frequency is now changed to 200 Hz c Calculate the impedance d Calculate the phase angle e Calculate the maximum voltage drop over each element

1 0 8 2 0 4 3 1 25 4 0 125 33 The phase difference between the alternating current an emf is n 2 Which of the following cannot be t constituent of the circuit Power FrimsX IN 1 Calone 2 R L 4 L alone A 3 L C 4 The reactance of a circuit is zero It is possible that circuit contains 3 D and C iv ii R and L iii R and C

The value of C if circuit becomes resonant after closing the key is 1 OL 3 L L voooooo V V sinot C 2 w C C 4 K 2 wo L C

7 An R L C circuit containing a 5292 resistor a 230 mH inductor and a 8 8 F capacitor is driven by an A C voltage source that has an amplitude of 150V and frequency v 80 Hz How much average power is dissipated by this circuit 1 Zero 3 39 3 W The rms valun 2 78 6 W 4 19 6 W

A capacitor of capacitance C is charged to potential and is connected in circuit as LC switch S is 6 shown in the figure Switch S is closed at r 0 After time opened while switch S is closed If initially both the switches were open and capacitor of capacitance 2C was uncharged If the maximum charge stored on 2C would Cro find k mm S L

In an oscillatory LC circuit Qo is the charge on the capacitor of capacitance C when the magnetic field linked with the inductor of inductance L is zero Analyse the following statements i The charge on capacitor increases onwards ii The polarity of the plates of the capacitor does not change iii Energy of L C as a system is always constant iv For Qo charge on capacitor current in the circuit is zero Which of the following is correct A only i C iii and iv only B ii and iii only D ii and iv only

For the ac circuit shown in the figure R 100 kQ and C 10 pF the phase difference between Vin and Vout is 90 at the input signal frequency of kHz V in R C www V V V out C A B A R www

A sinusoidal voltage Av 75 0 V sin 200t is applied to a series RLC circuit with L 70 0 mH C 155 0 F and R 42 0 0 a What is the impedance of the circuit b What is the maximum current in the circuit A

In the given AC circuit applied voltage V 10 sin wt the capacitive reactance is 2 5 Q the inductive reactance is 1 25 Q the resistance of resistor is 3 5 4 R www C The peak value of total current in amperes is AC y da del V 10 sin 1 250 R www momm L ta 2 5 5 a gladus s gadu 3 N 71 C mm moooo L V

A transformer has an input of 240 V to its primary coil of 150 windings a If the secondary coil has only 25 windings what type of transformer is it step up or step down why b What is the potential difference leaving the transformer Each question answered is worth K 4 T 6 C 8 A6

The output voltage taken across the resistance of a LCR series resonant circuit falls to half its peak value at a frequency of 200 Hz and again reaches the same value at 800 Hz The bandwidth of this circuit is A 200 Hz B 200 3 Hz C 400 Hz D 600 Hz

ung of a resistance of 4 92 and inductive reactance of 3 02 Find actor in the circuit 22015 7 44 A 5 A 100 V ac circuit with frequency 50 Hz is applied across a resistance of 10 92 and capacitor of 500 uF Find current and phase difference between voltage and current 20

In the circuit shown below the key K is closed at t 0 The current through the battery is VR R V V A at t 0 and at t K R R R B C D R V R at t 0 and at t 0 and V R R R R VR R R R V R V R R at t 0 and R R at t at t co att L R R 2010

A box P and a coil Q are connected in series with an AC source of variable frequency The EMF of source is constant at 10V Box P contains a capacitance of 1uF in series with a resistance of 320 Coil Q has a self inductance 4 9mH and a resistance of 68 The frequency is adjusted so that the maximum current flows in P and Q Find the impedance of P and Q at this frequency Also find the voltage across P and Q respectively 769 989 7 6V 9 8V

7 A radio is tuned to station in the 30 MHz to 54 MHz What is corresponding wavelength band NCERT Pg 281 1 AM band 2 FM band 3 Short band as Four

15 Consider a series LCR circuit in which reactance each and resistance are 100 When the circuit is connected to ac source 220 V 50 Hz then current drawn from the source is NCERT Pg 245 1 2 2 2 A 2 1 1 2 A