Network Analysis and Synthesis, 1st Edition by Pearson

R–L–C Circuits and Resonance 169

I

X

= I sin f

=

=

V

Z

X

Z

I

VX

Z

L

X

L

2

or

Z

VX

I

2

=

L

X

(4.4)

II

V

Z

V

VX

V

X

I

I

Xy

L/ L

X

X

22

2

2

2

+=

==

or

II

V

X

I

XY

L

X

22

0+- =

Adding

V

X2

2

L













on both sides, we get the following form:

I

V

X

I

V

X

X

L

y

L

-













+=













22

2

2

2

This equation is of the form:

(x - a)

2

+ y

2

= r

2

This is the equation of a circle.

In this case, the radius of the circle is

V

X2

L

and the centre of the circle is at

V

X

O

2

L

,













.

This proves that the locus of the current in an R-L series circuit, where R is variable is a

circle. This locus is also called the circle diagram. For an R-C circuit with variable R, the locus

of current will also be a circle.

Similarly, one can draw the locus ...