Question #170648

A coil with resistance ‘

6

’

Ω

,

and

inductance

‘

8

’ mH

is connected

in parallel

with a

series

combination of

a

resist

or and

capacitor

having

resistance R

Ω and

reactance X

c

Ω.

If

t

he equivalent

impedance

of the resulting circuit is

Z =

5

/0

o

Ω at

ω

=1000 rad/sec

. Find the

values of R & C

.

Expert's answer

Given, "Z_L = 6+j8"

It is connected across "R-jX"

The resultant parallel combination yields

"5\\angle0" .

i. e"\\frac{(6+j8) (R-jX) }{(6+R) +j(8-X)} =5+j0"

Simplifying and equating real and imaginary parts, we have,

"R+8X=30 \\newline\n8R-X=40"

Solving we have

"R= 5.38\\Omega\\newline X=3.077\\Omega \\newline \nAlso Z = 5.38-j3.07"

Also "X=1\/C\\omega\\implies C=0.325\\mu F"

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