In a parallel electrical circuit the impedance Z can be calc

In a parallel electrical circuit the impedance Z can be calculated using the equation

Upper Z equals StartStartFraction 1 OverOver StartFraction 1 Over Upper Z 1 EndFraction plus StartFraction 1 Over Upper Z 2 EndFraction EndEndFractionZ=11Z1+1Z2

where

Upper Z 1Z1

and

Upper Z 2Z2

are the impedances for the branches of the circuit. If

Upper Z 1 equals 80 plus 65 iZ1=80+65i

and

Upper Z 2 equals 40 plus 30 iZ2=40+30i,

calculate Z.

Solution

In parallel impednace circuit :

Z = (Z1*z2/(z1 + z2)

z1 = 80 + 65i ; z2 = 40 +30i

So, Z = (80+65i)(40 +30i)/(120+ 95i)

= ( 3200 + 240i + 2600i - 1950)/(120 +95i)

= ( 1250 + 2840i)/(120 + 95i)

Rationalise denominator by mulitplying num and den. with ( 120 - 95i)

So, z = ( 1250 + 2840i)( 120 - 95i)/ 23425