Tiêu đề 23. Alternating Current Hard.pdf ✅

1. A small loop lies outside a circuit. The key of the circuit is closed and opened alternately. The closed loop will show (a) Clockwise pulse followed by another clockwise pulse Clockwise pulse followed by another clockwise pulse (b) Anticlockwise pulse followed by another anticlockwise pulse (c) Anticlockwise pulse followed by a clockwise pulse (d) Clockwise pulse followed by an anticlockwise pulse 2. In an ac dynamo, the number of turns in the armature are made four times and the angular velocity 9 times, then the peak value of induced emf will become (a) 36 times (b) 12 times (c) 6 times (d) 18 times 3. Primary voltage is Vp, resistance of the primary winding is Rp. Turns in primary and secondary are respectively Np and Ns then secondary current in terms of primary voltage and secondary voltage respectively will be (a) 2 2 , p s s p p s p p R N V N R N V N (b) 2 2 2 2 , p s s p p s p p R N V N R N V N (c) 2 2 2 2 , p s s p s p p R N V N R N V N (d) p s s p p s p p R N V N R N V N 2 2 2 2 , 4. The equation of an alternating current is i = 50 2 sin 400t ampere then the frequency and the root mean square of the current are respectively (a) 200 Hz, 50 amp (b) 400  Hz, 50 2 amp (c) 200 Hz, 50 2 amp (d) 50 Hz, 200 amp 5. What will be the equation of ac of frequency 75 Hz if its r.m.s. value is 20 A (a) i = 20 sin 150 t (b) i = 20 2 sin(150 t) (c) sin(150 ) 2 20 i =  t (d) i = 20 2 sin(75 t) 6. The instantaneous value of current in an ac circuit is i = 2 sin(100 t +  / 3)A. The current at the beginning (t = 0) will be (a) 2 3 A (b) 3 A (c) A 2 3 (d) Zero 7. The voltage of an ac source varies with time according to the equation V = 100 sin(100t) cos(100t) where t is in seconds and V is in volts. Then (a) The peak voltage of the source is 100 volts (b) The peak voltage of the source is 50 volts (c) The peak voltage of the source is 100 / 2 volts (d) The frequency of the source is 50 Hz 8. If the frequency of ac is 60 Hz the time difference corresponding to a phase difference of 60o is (a) 60 sec (b) 1sec (c) sec 60 1 (d) sec 360 1 9. The r.m.s. value of the alternating e.m.f. E = (8 sin t + 6 sin 2 t) V is (a) 7.05 V (b) 14.14 V (c) 10 V (d) 20 V 10. Voltage and current in an ac circuit are given by       = − 6 5 sin 100  V  t and       = + 6 4 sin 100  i  t (a) Voltage leads the current by 30° (b) Current leads the voltage by 30° (c) Current leads the voltage by 60° (d) Voltage leads the current by 60° 11. The instantaneous values of current and potential difference in an alternating circuit are i = sin t and E = 100 cos t respectively. r.m.s. value of wattless current (in amp) in the circuit is (a) 1 (b) 1 / 2 (c) 100 (d) Zero 12. The r.m.s. current in an ac circuit is 2 A. If the wattless current be 3A , what is the power factor (a) 3 1 (b) 2 1 (c) 2 1 (d) 3 1 13. r.m.s. value of alternating current in a circuit is 4 A and power factor is 0.5. If the power dissipated in the circuit is 100W, then the peak value of voltage in the circuit is (a) 50 volt (b) 70 volt (c) 35 volt (d) 100 volt 14. The impedance of an ac circuit is 200  and the phase angle between current and e.m.fis o 60 . What is the resistance of the circuit (a) 50  (b) 100  (c) 100 3 (d) 300  15. An alternating voltage E = 200 2 sin(100 t) is connected to a 1 microfaracd capacitor through an ac ammeter. The reading of the ammeter shall be (a) 10 mA (b) 20 mA (c) 40 mA (d) 80 mA 16. An 120 volt ac source is connected across a pure inductor of inductance 0.70 henry. If the frequency of the source is 60 Hz, the current passing through the inductor is (a) 4.55 amps (b) 0.355 amps (c) 0.455 amps (d) 3.55 amps S + –
17. The current and voltage in an ac circuit are respectively given by i = sin 314 t and e = 200 sin (314 t +  / 3) If the resistance is 100, then the reactance of the circuit is (a) 100 / 3 (b) 100 3 (c) 200  (d) 200 3 18. When 100 volt dc is applied across a solenoid, a current of 1.0 amp flows in it. When 100 volt ac is applied across the same coil, the current drops to 0.5 amp. If the frequency of ac source is 50 Hz the impedance and inductance of the solenoid are (a) 200 ohms and 0.5 henry (b) 100 ohms and 0.86 henry (c) 200 ohms and 1.0 henry (d) 100 ohms and 0.93 henry 19. A sinusoidal voltage Vosint is applied across a series combination of resistance R and inductor L. The amplitude of the current in the circuit is (a) 2 2 2 o R L V +  (b) 2 2 2 o R L V −  (c) 2 2 2 o R L V +  sint (d) Vo/R 20. An ideal choke takes a current of 8 A when connected to an a.c. source of 100 volt and 50Hz. A pure resistor under the same conditions takes a current of 10A. If two are connected in series to an a.c. supply of 100V and 40Hz, then the current in the series combination of above resistor and inductor is (a) 10A (b) 8A (c) 5 2 amp (d) 10 2 amp 21. A resistor R, an inductor L and a capacitor C are connected in series to a source of frequency n. If the resonant frequency is nr then the current lags behind voltage, when (a) n = 0 (b) n < nr (c) n = nr (d) n > nr 22. An electron moves along the line AB which lies in the same plane as a circular loop of conducting wire as shown in figure. What will be the direction of current induced if any in the loop - A e – v B (a) No current will be induced (b) Induced current will be clockwise (c) Induced current will be anti clockwise (d) The current will change direction as the electron passes by 23. A 50 Hz ac source of 20 volts is connected across R and C as shown in figure. The voltage across R is 12 volt. The voltage across C is – R C  (a) 8 V (b) 16 V (c) 10 V (d) Not possible to determine unless values of R and C are given 24. An AC ammeter is used to measure current in a circuit. When a given direct current passes through the circuit, the AC ammeter reads 3 ampere. When another alternating current passes through the circuit, the AC ammeter reads 4 ampere. Then the reading of this ammeter if DC and AC flow through the circuit simultaneously, is - (a) 3 amper (b) 1 ampere (c) 7 ampere (d) 5 ampere 25. If i1 = 3 sin t and i2 = 4 cost, then i3 is– i3 i1 i2 (a) 5 sin (t + 53o) (b) 5 sin (t + 37o) (c) 5 sin (t + 45o) (d) 5 cos (t + 53o) 26. For An alternating current : (a) R.m.s value may be equal to peak value (b) Average value may be equal to peak value (c) R.m.s value may be equal to average value (d) All of the above 27. A circuit element is placed in a closed box. At time t = 0, a constant current generator supplying a current of I amp is connected across the box. Potential diff. across the box varies according to graph as shown in the figure. The element in the box is- 3 2 8 Volts (V) Time t(sec) (a) A resistance of 2 (b) A battery of emf 6V (c) An inductance of 2H (d) A capacitance 28. In the given circuit the average power developed is–
~ L = 0.2 H R = 50  V = 200 sin(250 t) volt (a) 50 2 watt (b) 200 watt (c) 150 2 watt (d) 200 2 watt 29. An inductor 10 /600 is connected to a 5 resistance in series. Find net impedance – 5 r XL (a) 15  (b) 12  (c) 13.2  (d) 18  30. An LCR series circuit with 100  resistance is connected to an AC source of 200 V and angular frequency 300 radians per second. When only the capacitance is removed, the current lags behind the voltage by 60o. When only the inductance is removed, the current leads the voltage by 60o. Then the current and power dissipated in LCR circuit are respectively (a) 1A, 200 watt (b) 1A, 400 watt (c) 2A, 200 watt (d) 2A, 400 watt 31. Find the rms value of the saw tooth wave form shown in figure - –1 0 0.5 2 t 2 –2 f(t) 1 (a) 5 (b) 1.15 (c) 4 (d) None of these 32. If resistance of 100  and inductance of 0.5 henry and capacitance of 10 × 106 farad are connected in series through 50 Hz A.C. supply, then impedance is - (a) 1.8765  (b) 18.76  (c) 187.6  (d) 101.3  33. In an a.c. circuit V and I are given by V = 100 sin (100 t) volts I = 100 sin (100 t + /3) mA the power dissipated in the circuit is- (a) 104 watt (b) 10 watt (c) 2.5 watt (d) 5.0 watt 34. In an A.C. circuit, a resistance of R ohm is connected in series with an inductance L. If phase angle between voltage and current be 45o, the value of inductive reactance will be - (a) R/4 (b) R/2 (c) R (d) Cannot be found with given data 35. The power dissipated in the adjacent circuit is – XL = 3R ~ R V = V0 sin t XC =R (a) R V 2 0 (b) 5R V 2 0 (c) 5R V 2 0 (d) 10R V 2 0 36. In a transformer Np = 500, Ns = 5000. Input voltage is 20V and frequency is 50Hz. What are the output voltage and frequency- (a) 200 V, 40 Hz (b) 100 V, 50 Hz (c) 200 V, 50 Hz (d) 150 V, 40 Hz 37. In adjacent circuit the instantaneous current equation is– R= 100  ~ L=1H V=200sin 100t (a) 2 sin        − 4 100t (b) 2 sin        − 4 100t (c) 2 sin        − 4 200t (d) 2        + 4 100t 38. The reading of the ammeter and voltmeters are (Both the instruments are ac meters and measures rms value) - Xc = 2 V A ~ 110V XL = 2 R = 55 (a) 2A, 110 V (b) 2A, 0V (c) 2A, 55V (d) 1A, 0 V 39. An alternating current is given by i = i1cost + i2sint. Thus rms current is given by (a) 2 i i 1 + 2 (b) 2 | i i | 1 + 2 (c) 2 i i 2 2 2 1 + (d) 2 i i 2 2 2 1 + 40. A resistance of 20 ohm is connected to a source of an alternating potential V = 220 sin (100t). The time taken by the current to change from its peak value to rms value is- (a) 0.2 sec (b) 0.25 sec (c) 25 × 10–3 sec (d) 2.5 × 10–3 sec
41. In an ac circuit V and I are given by V = 150 sin (150 t) V and I = 150 sin        + 3 150t A The power dissipated in the circuit is (a) 5625 W (b) 4825 W (c) 7450 W (d) 3425 W 42. In an ac circuit, V and i are given by V t volts i t mA      = = + 3 100sin(100 ) ,and 100sin 100  The power dissipated in circuit is (a) watt 4 10 (b) 10 watt (c) 2.5 watt (d) 5 watt 43. In a circuit an alternating current and a direct current are supplied together. The expression of the instantaneous current is given as i = 3 + 6 sint . Then the r.m.s. value of the current is (a) 3A (b) 6A (c) 3 2 A (d) 3 3 A 44. F  2.5 capacitor and 3000-ohm resistance are joined in series to an ac source of 200 volt and 1 50 − sec frequency. The power factor of the circuit and the power dissipated in it will respectively (a) 0.6, 0.06 W (b) 0.06, 0.6 W (c) 0.6, 4.8 W (d) 4.8, 0.6 W 45. A telephone wire of length 200 km has a capacitance of 0.014 F per km. If it carries an ac of frequency 5 kHz, what should be the value of an inductor required to be connected in series so that the impedance of the circuit is minimum (a) 0.35 mH (b) 35 mH (c) 3.5 mH (d) Zero