Hot Wire Instruments

       The hot wire instruments are based on the principle that length of wire increases due to heating effect when a current passed through it. It is a square law device with a non-linear relationship because increase in length of a wire is directly proportional to the square of current passing through wire. Note that the increase in the length of a wire is very small percentage of the total length of wire. Hence various mechanical linkages have been devised to expand this effect and convert it into motion of a point of a circular scale.

1.1 Construction and Operation of Hot Wire Instrument

       The constructional details of a hot-wire double sag type instruments are as shown in the Fig. 1.

       A hot working wire denoted by W in the Fig.1 is made up of  platinum-irridum alloy. The main advantages of using platinum-irridum alloy is that it can withstand high temperatures without deterioration of wire material caused by oxidation. The working wire W is very fine and its diameter is of the order of 0.1 mm. The wire W is stretched between two point A and B where point B is fixed point and point A is tension adjustment point at which tension adjustment mechanism is placed. One more wire W₁, made up of phosphor-bronze is connected to main hot wire W at point C while other end of wire W₁ is connected to fixed point D. A fine thread of silk material represented by G is connected between spring S and point F. The thread G is wound around a pulley denoted by E. Both points F and spring S are fixed points. A point P used for indication and thin aluminium disc L are mounted on the spindle. The pulley system E is also mounted on the spindle.

       When a current to be measured is passed through the wire, it gets expanded as a result of heating effect by current flowing through it. Because of heating effect, a sag is produced in the wire W. Now the sag in main working wire W causes sag in other wire W₁. This sag is transferred to the spring S through a fine silk thread G. Thus the sag produced gets magnified and the spring activates pulley to rotate and pointer gets deflected indicating value of the current under measurement on a graduated scale.

       The expansion of the wire is proportional to the heating effect of the current. As heat produced is in the form of power dissipated give P = I²R , the expansion of the wire in hot wire instrument is proportional to the square of r.m.s. value of the current. A thin aluminium disc L rotates between poles of the permanent magnet M and it provides eddy current  damping to the instrument. The base of the main instrument is made up of a material which is having coefficient of expansion same as that of hot wire. As base and hot wire, both have same coefficient of expansion, the errors due to uneven expansion between base of instrument and hot wire are minimized.

       In early hot wire instruments, the hot wire used was made up of platinum-silver alloy. But the main drawback of early instruments was the low value of the full-scale operating temperature ( about 135-150 ^oC). Because of very low operating temperature, even small variations in room temperature affects the position of the pointer. Today's hot wire instruments use wire made up of platinum-irridum alloy with which operating temperature range can be extended upto 300 to 500 ^oC. As the temperature range is increased, the effects due to room temperature variations are minimized. The hot wire is made very thin so that it can attain steady temperature quickly when current flows through wire. The size of wire is decided such that it can bare normal mechanical stresses developed in the instruments.

       The hot wire instrument can be used as ammeter over a range 0 to 1 A without a shunt, while 0 to 5 A with a shunt. It can be used as a voltmeter to measure voltage upto 400 V by using high value non-inductive resistance in series with instruments.

1.2 Derivation of Magnification Factor

       Let us assume that the length of the hot wire be l.

Fig.1 Sag in main hot wire W

       Let the increase in wire length due to the heating effect by current I to be measured be δl. The sag in the wire due to expansion is given by,

But δl is fractional value and its square value is smaller than itself. Hence neglecting &l term, the sag in wire is given by,

       But δl is fractional value and its square value is smaller than itself. Hence neglecting δ²l term, the sag in wire is given by,

       The magnification factor M is given by,

       To achieve further magnification, a phosphor-bronze wire of length L₁is connected at the center of wire W stretched between points A and B as shown in the Fig.2.

Fig.2 Arrangement of extending magnification

       Let the sag in new wire be S₁and it is given by,

       Now S is also a fractional value so neglecting higher order term is S i.e. S², we get,

       Substituting value of S from equation (3), we get,

       Thus the magnification factor is given by,

1.3 Advantages
       The advantages of hot wire instruments are as follows:

1.In hot wire instruments, the deflection of instrument is measured in terms of the r.m.s. current flowing through the wire irrespective of its frequency or waveform. Thus it can be used in a.v. as well as d.c. systems. The reading of the instrument is independent of frequency and waveform of the current to be measured.

2. The operation is not based on any magnetic effect, hence the instrument is free from stray magnetic field.

3. In a.c. as well as d.c. systems, the calibration is not different.

4. The error due to temperature variations are not much significant. with suitable adjustments these errors can be eliminated.

5. This instrument can be used for current measurements at very high frequencies.

6. It is fairly accurate instrument.
7. Its construction is very simple and it is cheaper.
1.4 Disadvantages
       The disadvantages of hot wire instruments are as follows.

1. The instrument is not able to withstand overloads because wire is so fine and it may melt before any protection circuit operates.

2. Similar to moving iron type instruments, its scale is uneven.

3. It consumes verly high power.
4. The instrument is delicate.
5. As the time is elasped in heating working wire, the response of the instrument is slow.
6. Due to temperature variations in the surroundings, it is necessary to adjust zero position frequently.
7. The instrument does not provide same deflection for ascending and descending values.