Question

The opposition to current in an electrical circuit is called its impedance. The impedance z in a parallel circuit with two pathways satisfies the equation: 1/z + 1/z1 + 1/z2 where z1 is the impedance (in ohms) of pathway 1 and z2 is the impedance of pathway 2.

a) The impedance of each pathway in a parallel circuit is found by adding the impedances of all components in the pathway. Use the table to find z1 and z2.
b) Find the impedance z.
(diagram drawn)

Answer 1

a 1/z1 = 1/bi

1/z2 = -1/ci

b impedance z = 1/z = [(1/a)² + (-1/ci -1/bi)²]^1/2

Explanation:

circuit in parallel

a for the resistor impedance = 1/z = 1/ a

for the inductor inductance = 1/ bi = 1/xL

for the capacitor capacitance = - 1/ci = 1/xc

the reactances is the INDUCTANCE AND CAPACITANCE

The impedance = 1/z = [ (-1/ci -1/bi)²]^1/2

Since the circuit is parallel impedance z across the pathway is given by

b impedance z = 1/z = [(1/a)² + (-1/ci -1/bi)²]^1/2