Question

a series LCR circuit with L=0.12H , C=4.8×10-7F, R =23ohm connected to a variable frequencysupply . At what frequency is the current maximum​

Answer 1

Answer:

Explanation:

a)

V  

o

​  

=  

2

​  

V=325.2 volts

Tt resonance, ω  

R

​  

L=1/(ω  

R

​  

C)

We know that,  

⇒ω  

R

​  

=1/  

LC

​  

 

=4166.67rad/s

Resonant frequency,

ν  

R

​  

=ω  

R

​  

/2π

=663.48Hz

I  

o

​  

=V  

o

​  

/R=14.14A

(b)

Maximum power absorbed

P=  

2

1

​  

I  

o

2

​  

R

2

1

​  

(14.14)  

2

×23

⇒2299.3W

(c)

The angular frequencies at which the power would be half of the power at resonant frequency will be:

ω  

′

=ω  

R

​  

 ±Δω

Here, Δω=  

2L

R

​  

 

⇒Δω=  

2×0.12

23

​  

 

⟹95.83 rad/s

So,

ω  

1

′

​  

=4166.67+95.83

=4262.3 rad/s

ω  

2

′

​  

=4166.67−95.83

=4070.87 rad/s

The amplitude of current at these frequencies will be the RMS value.

I=  

2

​  

 

I  

0

​  

 

​  

 

⇒  

1.414

14.14

​  

 

⇒10 A

(d)

Q factor is given by  

Q=  

R

1

​  

 

C

L

​  

 

​  

=  

23

1

​  

 

480×10  

−9

 

0.12

​  

 

​  

=21.74