Basic_Electrical_Engineering_4th_edition

86	ELECTRICAL ENGINEERING

The original equivalent circuit is

						Fig. E1.16 (a)
	Z0 = Q Xco = 50 x 2 = 100 kQ
The bandwidth		=	{0			1000	= 20 kHz
			- --				2 kQ
			Q			50
The equivalent circuit with				loading resistance is
					=
	Q' xco = 40					Fig. E1.16 (b)
						100	200
	Q'	=		7		2 == 7
					140		7
Therefore,			200x			2	100
Therefore, bandwidth =			1000
			100x x 7 = 70 kHz

It is to be noted that bandwidth in case of parallel resonance is obtained when net impedance of the circuit is 70.7% of the maximum value.

For a parallel RLC circuit

y	=
m

Since Q0 = m0 CR we have
Y.	=
m	=

the admittance is given as

]	+ j		(roe-	--1			J
R	+ j			roL
]		( o0C			_				J
			ror	R
R			ro0R				rom0L
				R		_		ro0R
]__ +l_ ((l)(1)0C								roro0 LJ
R	R		ro0

.

.

.

(1.42)

...(1.43)

A-C CIRCUITS								91
	The resistance required for shunting is say R'
			58800	=	147000R'
or		x			147000			R'
	147000		58800	=	147000		x+	58800
or			R'
				=		88200
				= 98
						kn.	Ans.

1 . 1 1 MAGNETIC CIRCUITS

Oersted in 1819 discovered that a current flowing in a straight conductor deflected the needle of a compass and it shows that the paths of magnetic force are concentric circle around the conductor. Similarly if a current is passed through circular (loop) conductor the magnetic flux are found to be concentric to the circularconductor and the magnetic flux density at the centre of the circular conductor is given by (loop)

tl

B = 2 r

where B is the magnetic flux density in Wb/m2 orin Tesla, I the current flowing through the circular loop of the conductor and r the radius of the circular loop, t the permeability of the material around which the loop is wound.

µ = µ0 = 4n x 10-7 Him

if the coil is wound on a non-magnetic material or it is air cored and µ = µ0 µ,.

where µ,. is the relative permeability of the magnetic material. The magnetic flux density is related to magnetic field intensity through µ as given below.

B = µ0 µ,. H

where H is the magnetic field intensity and its units are Ampere turns per meter. µ,. has no units as it is a relative permeability,µ is permeability ofthe material and its units are Henry/m.

We know that the electrostatic potential Vand electric field intensity are related by E = - VV

Similarly, the scalar magnetic potential Vm is related to magnetic field intensity H as H = - VVm

In dealing with magnetic circuits it is convenient to call Vm the magnetomotive force or mmf as it has analogy with electromotive force in electric circuits-Just as an electromotive force drives the electric current or conventional current through a conductor the magnetomotive force similarly creates and drives magnetic flux through a magnetic material or in space. The units of mmf are ampere-turns when current is passed through N no. of coils or turns of a conductor.

The electric potential difference between two points is given as