Question

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

.

Answer 1

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,

$R+8X=30 \newline 8R-X=40$

Solving we have

$R= 5.38\Omega\newline X=3.077\Omega \newline Also Z = 5.38-j3.07$

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