Question

What is the impedance of the following circuit when connected to d.c ?

Answer 1

Answer:

For an L-C-R circuit, the impedance (Z) is given by

∵Z=  

R  

2

+(X  

L

​  

−X  

C

​  

)  

2

 

​  

 

where, X  

L

​  

=ωL=2πf  

1

​  

 

and X  

C

​  

=  

ωC

1

​  

=  

2πfC

1

​  

 

Given, f=  

π

50

​  

Hz, R=300Ω and L=1H

and C=20μC=20×10  

−6

C

      Z=  

(300)  

2

+  

⎝

⎜

⎜

⎛

​  

2π×  

π

50

​  

×1−  

2π×  

π

50

​  

×20×10  

−6

 

1

​  

 

⎠

⎟

⎟

⎞

​  

 

​  

 

     Z=  

90000+(100−500)  

2

 

​  

 

⇒Z=  

90000+160000

​  

=  

250000

​  

 

⇒Z=500Ω

Hence, the current in the circuit is given by

i=  

Z

V

​  

=  

500

50

​  

=0.1A

Voltage across capacitor is

V  

C

​  

=iX  

C

​  

=  

2πfC

i

​  

=  

2π×  

π

50

​  

×20×10  

−4

 

0.1

​  

 

             =  

100×20

0.1×10  

6

 

​  

⇒V  

C

​  

=50V

Explanation: