A Series L-C-R circuit Having L = 1.5 H,  is Connected To A 200-V a.c. Supply Of Variable Frequency. When The Supply Frequency Equals The Natural Frequency Of The Circuit, Find The Average Power Transferred To The Circuit In One Full Cycle. 

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Question

A series L-C-R circuit having L = 1.5 H,  is connected to a 200-V a.c. supply of variable frequency. When the supply frequency equals the natural frequency of the circuit, find the average power transferred to the circuit in one full cycle. 

Solution

Correct option is

2000 W

The natural (angular) frequency of the L-C-R circuit is 

            

When an a.c. voltage of angular frequency  = 138 Hz is applied to the circuit, we have 

      

and capacitive reactance, 

        

   

                                

This is the condition of resonance. The rms resonant current in the circuit is  

          

The power is transferred to the resistor only. Therefore  

        

Testing

SIMILAR QUESTIONS

Q1

An alternating rms current of 1.5 mA and angular frequency  flows through a  capacitor in series. Calculate the rms voltage across the capacitor and the impedance of the circuit.

Q2

When an alternating voltage of 220 V is applied across a device X, a current 0.5 A flows through the circuit and is in phase with the applied voltage. When the same voltage is applied across another device Y, again the same current flows but it leads the voltage by . Compute the current in the circuit when the same voltage in applied across the series combination of X and Y.

Q3

 capacitor in series with a  resistor is connected to a 110V-60 Hz supply. What is the maximum current in the circuit? What is the time lag between current maximum and voltage maximum?   

Q4

A 20 V-5 W lamp is to run on 200 V-50 Hz a.c. mains. Find the capacitance of a capacitor required to run the lamp.

Q5

An alternating emf of frequency 50 Hz is applied to a series circuit ofresistance , an inductance of 100 mH and a capacitance of . Does the current lag or lead the emf and by what angle?

Q6

 capacitor, a 0.10- H inductor and a 25.0- resistor are connected with an a.c. source of emf E = 310 sin 314t. Find the frequency of the emf.

Q7

A 100-V a.c. source of frequency 500 Hz is connected to a series LCRcircuit with L = 8.1 mH. Find the difference across the resistance.

Q8

 capacitor, a 0.3-H inductor and a  resistor are connected in series with a 120-60Hz a.c. source. Calculate the impedance of the circuit.

Q9

A circuit containing a 80-mH inductor and a 60- capacitor in series is connected to a 230 V-50 Hz supply. The resistance in the circuit is negligible. Obtain the current amplitude and rms current.  

Q10

An inductor L, a capacitor of  and the resistor of  are connected in series with an a.c. source of frequency 50 Hz. If the current is in phase with the voltage, calculate the inductance of the inductor.