Electrical impedance z is the ratio of voltage to current in

Electrical impedance, z, is the ratio of voltage to current in ac circuits. If there are two resistors in a circuit, let Z_1 = 3- 7i ohms and Z_2 = 5 + 4i ohms. Electrical Circuits in Parallel. When the resistors in the circuit are placed in parallel, the total impedance is given by g 1/Z = 1/z_1 + 1/Z_2 Find the total impedance of the electrical circuit in parallel. Enter the fully simplified answer in standard form. 1/Z =

Solution

z1 = 3 -7i ; z2 = 5 +4i

1/z = 1/z1 +1/z2

= 1/(3 -7i) + 1/(5 +4i)

= ( 5+4i +3 -7i)/(3- 7i)(5 +4i)

= ( 8 - 3i)/(3 -7i)( 5 +4i)

= (8 -3i)/( 15 +12i - 35i + 28)

= (8 -3i)/( 43 - 23i)

= ( 8 -3i)(43+23i)/( 43^2 +23^2)

= ( 344 + 184i - 129i +69)/2378

= 413/2378 + 55i/2378