help 2.3

Question

2.3.  a circuit consists of the following components:

Z1=110-j21, 21 ohms

Z2=150+j26, 41ohms

Z3=100+j46, 31ohms

 

If z1 and z2 are connected in parallel, and this combination is connected in series with z3 across a 240V, 50Hz supply. Calculate:

a. the total impedance of the circuit to ensure maximum power transfer

b. the current in different branches. Also draw the phasor diagram.

Answer 1

(a)

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.

Step 2:

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 .

Solution :

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

Answer 2

(b)

Step 1:

The supply voltage is  240V, 50Hz.

The total circuit impedance is .

So the circuit is .

The circuit current is .

Also the current through the is .

The polar form of the is .

Phasor diagram of the :

Step 2:

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 :

Comments

Step 3:

Find current in the :

The polar form of the is .

Phasor diagram of the :

Solution :

(i) Current through the is .

(ii) Current through the is .

(iii) Current through the is .