Step 1:

Circuit having 3 impedance components and source.

.

z1 and z2 are connected in parallel.

This combination is connected in series with z3 across a 240V, 50Hz supply.

Draw a circuit with above specifications :

Find the total impedance of the circuit.

z1 and z2 are connected in parallel.

is in series with z3.

According to maximum power transfer theorem, the maximum power will transfer only if load impedance equals to source impedance .

So the impedance of the circuit that ensure maximum power transfer is .

(b)

Step 1:

The supply voltage is  240V, 50Hz supply.

The total circuit impedance is .

So the circuit is .

The circuit current is .

Also the current in the is .

The polar form of the is .

Phasor diagram of the :

Observe the circuit the voltage in parallel loop is same.

So .

Find the drop across .

Voltage in parallel loop is .

Find current in the :

The polar form of the is .

Phasor diagram of the :

Find current in the :

The polar form of the is .

Phasor diagram of the :