## Three ammeter method for measurement of power:

Following figures shows the circuit diagram and phasor diagram of three ammeter method for measurement of power. The current measured by the ammeter A1, is the vector sum of the load current and that taken by the non-inductive resistor R, this latter being in phase with V.

From phasor diagram, we have:

• The advantage of this method is that the value of determined is independent of supply frequency and waveforms.
• The disadvantages of measurement of power by three voltmeter method are overcome in this method.

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

### Example 1:

The following readings were obtained from three ammeters used for a single phase power measurement: An inductive load takes a current of 2.5 A; a non-inductive resistor connected in parallel takes 2.4 A, when connected across 250 V supply. The total current taken from the supply is 4.5 A. Calculate:

a)    Power absorbed by the load.

c)     Power factor of the load.

### Solution:

Given: I3 = 2.5 A; I2 = 2.4 A; I1 = 4.5 A; V = 250 V.

Non-inductive resistance, R = (V/I2) = 250/2.4 = 104.17 Ω.

i)                  Power absorbed by the load, P:

P = (R/2)*(I1^2 – I2^2 – I3^2)

= (104.17/2)((4.5^2)-(2.4^2)-(2.5^2)) = 429.2 W     (Ans.)

Z = (V/I3) = (250/2.5) = 100 Ω   (Ans.)

iii)             Power factor of the load, cos ф = (I1^2 – I2^2 – I3^2) /2I2I3

= [(4.5^2)-(2.4^2)-(2.5^2)]/(2*2.4*2.5) = 0.687    (Ans.)

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Three voltmeter method for measurement of power.

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## 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 ф = (V1^2 – V2^2 – V3^3)/2V2V3

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

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## Four point starter:

In four point starters, the hold on coil is connected directly across the supply line through a protective resistance R. when the armature touches stud no 1.the line current divides into three parts i) armature starting resistance and overload release. ii) a variable resistance and shunt field winding. Iii) Holding coil and current limiting resistance.

The basic difference between three point and four point starters is the manner in which the hold on coil is connected. The unnecessary tripping of starter can be stopped by connecting separately or parallel both magnetizing and field coil. They are connected in such a way that both should carry their individual current. Thus voltage drop in one coil will not affect the voltage in other coil.