An a.c. circuit having an inductor and a resistor in series draws a power of 560 W from an a.c. source marked 210 V-60 Hz. The power factor of the circuit is 0.8. Calculate the impedance of the circuit and the inductance of the inductor. 


Correct option is

The average power over a complete cycle is given by 



The impedance of the circuit is 


The power is consumed in R only. Therefore    


Now, the impedance of an L-R circuit is 









A capacitor, a  resistor and a 80-mH inductor are in series with a 50-Hz a.c source. Calculate the capacitance if the current is in phase with the voltage. 


A series L-C circuit has L = 0.405 H and . The resistance R is zero. Find the frequency of resonance.    


In a series L-C-R circuit connected to a variable frequency 220-V source; we have : L = 4.0 H, . Calculate the resonant frequency of the circuit.   


A variable-frequency 230-V alternating voltage source is connected across a series combination of L = 5.0 H,  and . Calculate the angular frequency of the source which drives the circuit in resonance. 


A series LCR circuit with L = 0.12 H, C = 480 nF and  is connected to a 230-V variable-frequency supply. What is the source frequency for which current a amplitude is maximum? Find this maximum value.


An L C R circuit has L = 10 mH connected in series to a source of  volt. Calculate the current-amplitude and the average power dissipated per cycle at a frequency 10% lower than the resonant frequency. 


A 750-Hz, 20-V source is connected to a resistance of , an inductance of 0.1803 H and a capacitance of , all in series. Calculate the time in which the resistance (thermal capacity = 2 JoC–1) will get heated by 10oC. 


Obtain the resonant frequency and Q-factor of a series LCR circuit with L= 3.0 H. How will you improve the sharpness of resonance of the circuit by reducing its full width at half maximum by a factor of 2?  


A virtual current of 4 A flows in a coil when it is connected in a circuit having a.c. of frequency 50 Hz. The power consumed in the coil is 240 W. Calculate the inductance of the coil if the virtual p.d. across it is 100 V. 


A town situated 20 km away from a power plant generating power at 440 V, requires 600 kW of electric power at 200 V. The resistance of the two-wire line carrying power is  /km. The town gets power from the line through a 3000-220 V step-down transformer at a sub-station in the town. Estimate the line power loss as heat.