To Verify Three Voltmeter Method

Theory

Three Voltmeter Method

The 3-voltmeter method is used to measure the inductance, resistance, quality factor, and power absorbed of a choke coil. A choke coil can be represented as a pure inductance in series with an equivalent resistance that accounts for core losses and inherent resistance.

Three Voltmeter method for measurement of power:

The three voltmeter is used in an inductive circuit to measure the value of the power factor. As seen on Figure above , one voltmeter is used to measure the voltage of the circuit (Ui), the second one measures the voltage on the non-inductive resistance (UR) that is connected in the series with the load branch and the third voltmeter is used to measure the voltage of the load (Ut).

This concept is illustrated in following figures.

Three voltmeter method vector diagram

V1, V2 and V3 are the three voltmeters and R is a non-inductive resistance connected in series with the load as shown in figure.
From the phasor diagram, we have:

V₁² = V₂²+ V₃² + 2 V₂V₃CosΦ

but,
V₂ = I* R
V₁² = V₂²+ V₃² + 2 (I*R) V₃CosΦ


V₁² = V₂²+ V₃² + 2 R (V₃ICosΦ)


V₁² = V₂²+ V₃² + 2 PR


Since the power in Inductive Circuit,
P = V I₃CosΦ

or Power,
⇒P = ( V₁²- V₂²- V₃² ) \2R

Power factor of circuit is given by,

CosΦ = ( V₁²- V₂²- V₃² ) \ 2 V₂V₃