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Alternating Current 1. Write general equation for instantaneous e.m.f of a 60 cycle generator, whose peak voltage is 180 volt. 2. Find the time required for a 50 Hz alternating current to change its value from zero to the r.m.s. value ? 3. The electric current in a circuit is given by i = io (t/ ) for some time. Calculate the RMS current for the period t = 0 to t = A sinusoidal voltage V = 200 sin 314 t is applied to a resistor of 10 ohm. Calculate (i) r.m.s. value of voltage (ii) r.m.s, value of current (iii) power dissipated as heat in watt. 5. A pure inductor of self inductance 1 H is connected across an alternating voltage of 115 V and frequency 60 Hz. Calculate the (i) inductive reactance (ii) effective current (iii) peak current (iv) average power consumed. 6. An inductor (L = 200 mH) is connected to an a.c. source of peak EMF 210 V & frequency 50 Hz. Calculate the peak current. What is the instantaneous voltage of the source, when the current is at its peak value? 7. Calculate the capacitive reactance of a 5 F capacitor for a frequency of 50Hz. 8. A capacitor of 10 mF connected to an a.c. source of EMF E = 220 sin 100 t . Write the equation of instantaneous current through the circuit. What will be the reading of a.c. ammeter connected in the circuit. 9. A coil of resistance 300 ohm and inductance 1 H is connected across an alternating voltage of frequency 300/2 hertz. Calculate the phase diff. between voltage and current in the circuit. connected to 100Va.c. source, the current reduces to 0·5 A. Why is the current reduced in the latter case? Calculate the value of the reactance of the inductor? 12. When a series combination of inductance and resistance are connected with a 10 V, 50 Hz a.c. source, a current of 1A flows in the circuit. The voltage leads the current by a phase angle of /3 radian. Calculate the values of resistance and inductance. 13. A bulb of resistance 10 Ω, connected to an inductor of inductance L, is in series with an a.c. source marked 100 V, 50 hz. If the phase angle between voltage and current is π/4 radian, calculate the value of L? 14. A 80V-800 W heater is to be operated on a 100V50 hz a.c. supply. Calculate the inductance of the choke required. 15. A 100 mH inductor, a 25 µF capacitor and a 15 ohm resistor are connected in series to a 120 V, 50hz a.c. source. Calculate (i) impedance of the circuit at resonance, (ii) current at resonance (iii) Resonant frequency. 16. A 25·0 µF capacitor, a 0·10H inductor and a 25· 0 ohm resistor are connected in series with an a.c. source E = 310 sin 314 t. (i) what is the frequency of the e.m.f. ? (ii) calculate (a) the reactance of the circuit (b) the impedance of the circuit, and (c) current in the circuit. 17. A capacitor of 50 µF, a resistor of 10 ohm .and an inductor L are in series with an a.c. source of frequency 50 Hz. Calculate the value of L if phase angle between current and voltage is zero. 18. Find the capacity of a capacitor, which when put in series with a 10 ohm resistor, makes the power factor equal to 0·5. Assume an 80V-100 hz a.c. supply. 10. A 100 V, 50 Hz a.c. source is connected to a series combination of an inductance of 100 mH and a resistance of 25Ω. Calculate the magnitude and phase of the current. 19. A resistor of resistance 100 Ω is connected to an ac source, E = (12 V) sin (250π) t. Find the energy dissipated as heat during t = 0 to t = 1.0 ms. 11. When 100 volt d.c. is applied across an inductor, a current of 1A flows through it. If the same inductor is www.physicspaathshala.org