Adding resistor and capacitor in parallel

[obsolete]

Hi all,

I am meant to find the total impedance across the circuit but am having trouble with one section of the circuit. This section comprises of 2 resistors and 1 capacitor in parallel.

The two resistors are 8 ohms each and the capacitor is 3 ohms. So the process is meant to be:

Z = ( 1/8 + 1/8 + 1/j3) ^(-1)

and the answer is meant to be: 1.44 + j1.92

I know it is really simple but I can't wrap my head around it at the moment and it's driving me insane! Any help much appreciated.

 

[rl.bhat]

The secytion can be written as 4 ohms and 3j ohm are in parallel. Then
1/Z = 1/4 + 1/3j
Z = 12j /( 4 + 3j) . Now rationalise the denominator and simplify.

 

[obsolete]

Thanks rl.bhat.

I am wondering though how did you get 12j for the numerator? I'm sure it relates to 4 x 3j = 12j somehow but I'm not sure why...

 

[rl.bhat]

When you add 1/4 + 1/3j you get (3j + 4)/12j. This is 1/Z. therefore
Z = 12j/(4 + 3j)

 

[obsolete]

Thanks a lot man!