Consider a series R-L circuit with a variable R as shown in the Fig. 1. It is excited by an alternating source of V volts. The frequency of the source is f Hz.

Fig. 1 |

Let I = Current flowing through the circuit

Z = Impedance of the circuit

Z = R + j X

_{L}where X_{L}= 2 fL Now R is variable while X

_{L}is fixed. The phasor diagram is shown in the Fig. 2(a). The current I lags voltage V by angle as the circuit is inductive. The impedance triangle is shown in the Fig. 2(b).

Fig. 2 |

From the impedance triangle we can write,

sin Φ = X

_{L}/Z Substituting in the expression for I,

I = (V/X

_{L}) sinΦ ..............(1) This is the equation of a circle in polar co-ordinates with a diameter equal to (V/X

_{L}). When the resistance R =0, then Φ = 90

^{o}hence sin Φ = 1.**.**I = I

^{.}._{m }= (V/X

_{L})

This is the maximum value of current.

As R resistance, the phase angle decreases thus decreasing sin. Effectively current I also decrease. When R

**→**∞ the Φ**→**0^{o}and current becomes zero. The locus obtained of extremities of a current phasor plotted for various values of R is a semicircle. The semicircle is shown in the Fig. 3. The voltage axis is taken as vertical axis as a reference, with respect to which the various current phasors are plotted.

Fig. 3 Circle diagram |

The power factors at various conditions are cosΦ

_{1}, cosΦ_{2 }etc. As Φ varies only from 0^{o}to 90^{o}, the diagram is semicircle, infact it is a half part of a circle hence it is known as circle diagram. This theory of series R-L circuit can be easily extended to a three phase induction motor.

__Related articles :__**Circle Diagram : Introduction****Circle Diagram of a 3 Phase Induction Motor****No Load Test****Blocked Rotor Test****Construction of Circle Diagram****Load Tets on Three Phase Induction Motor**

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