Total Impedance

Question

Answer 1

Step 1:

Find the mutual inductance of and .

Mutual inductance is .

.

Draw equivalent circuit for coil 1: .

Draw equivalent circuit for coil 2: .

Capacitive impedance is .

Step 2:

Redraw the circuit:

Observe the circuit:

is in series with .

Equivalent impedance at coil 1 is

Equivalent impedance at coil 1 is .

is in series with and .

Equivalent impedance for coil 2 is

Equivalent impedance at coil 2 is .

Step 3:

Redraw the circuit:

Observe the circuit:

is in parallel with .

Step 4:

Redraw the circuit:

Observe the circuit:

is in series with and .

Total impedance of the circuit is .

can be written in polar form as .

Solution:

Total impedance of the circuit is .