# Q: Derive the relation between phase voltage and line voltage in case of balanced star connected load.

# OR

# Derive an expression for total power input for n balance 3 phase load in terms of line quantities and power factors.

**Star-connection**

As show in figure given below, three equal impedances (load) are also connected in star across star-connected supply. If all the 3 impedances arc equal, then it is known as balanced load.

All the three voltages will have same magnitude but 120^{0} phase difference. These voltages are measured between neutral and phase points (i.e. R, Y, B) and hence known as phase voltages (V ph ). Three more combinations are also possible. These arc voltages between (i) pts. R and Y V_{RY} (ii) pts. Y and B,V_{YB} (iii) pts. B and R, V_{BR} . These are known as line voltages ( V_{L }) .

**Relation between** ** **V_{L} and V_{ph}

Phasor diagram for the phase voltages will be as shown below. We will calculate any one of the line voltage. V_{RY} is the voltage between R and Y .From the figure,

Hence, V_{RY} is obtained by adding ( -V_{Y} ) and The resultant V_{RY} will be 30^{0} ahead of V_{R} . Hence, V_{L} is 30^{0} ahead of V ph . The magnitude of V_{RY} can be calculated as,

Hence, magnitude of line voltage is magnitude under root 3 of phase voltage.

**Relation-between I**_{L} and I_{ph}

_{L}and

The three currents I_{R} , I_{Y} and I_{B} can be calculated as,

Hence, all the three currents have same magnitude but 120^{0} phase difference Now, current through neutral wire ( I_{N}) will be the sum of all the three currents.

Expression for power : For 3-phase load

Total power , P = 3 phase power

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