 # Three voltmeter method

## Three voltmeter method for measurement of power:

As we know, wattmeters are used for measurement of power in inductance AC circuits, but in some cases it is not possible to use wattmeters because of their incorrect readings or sometime wattmaters may not available. So in such cases three voltmeters or three ammeter method is used for measurement of power.

### Three voltmeter method:

Following figure shows the circuit diagram for three voltmeter method.

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: The assumptions are made that the current in the resistor R is same as the load current.

• Supply voltage higher than normal voltage is required because an additional resistance R is connected in series with the load Z (inductive circuit).

• Even small errors in measurement of voltages may cause serious errors in the value of power determined by this method.

Let us solve one simple numerical example based on three voltmeter method for clear understanding.

### Example 1:

The following readings were obtained from three voltmeters used for a single phase power measurement:

V2 = 180 voltas across a non-inductive resistaor; V3 = 200 volts across an inductive load; V1 = 300 volts across the two in series.

Calculate the power factor of the inductive load.

### Solution:

Given: V2 = 180 V; V3 = 200 V; V1 = 300 V

Power factor, cos ? = (V1^2 – V2^2 – V3^3)/2V2V3

Or cos ? = [(300^2) – (180^2) – (200^2)]/(2*180*200) = 0.244   (Ans.)

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