## AC Polar Type Potentiometer :

#### The Drysdale Tinsley AC Potentiometer is a polar-type potentiometer, which measures the magnitude (V) in one scale and phase (θ) in another scale. The complete connection diagram of the Drysdale Tinsley ac potentiometer is shown below.

#### Where,- T.I. - Transfer instrument (precision type electro-dynamometer ammeter)
- DPDT - Double pole double throw
- SPDT - Single pole double throw
- G - D'Arsonval galvanometer
- VG - Vibration galvanometer
- B - Standard battery
- POS 1 - position 1
- POS 2 - position 2

When an ac voltage measurement is done by taking a reference ac voltage supply, the conditions that must be satisfied are,- Both the voltages should have same frequency.
- Their phases should be same.
- Their magnitudes should also be same at all the instants.

It is very difficult to satisfy all three conditions if we use a separate reference source. Hence, in this instrument we connect the unknown ac voltage to a phase-shifting transformer whose one stator winding is connected directly to the unknown supply and the other stator winding is connected to the same supply through a variable resistor and a capacitor.

By varying the resistance and capacitance of the second winding, the current through it can be made exactly in quadrature with the supply. This results in the production of a rotating magnetic field (RMF) (i.e., due to phase splitting) which links with the rotor winding to induce an emf in it with the same frequency as that of supply and whose phase angle can be selected by changing the rotor position. Hence, the phase angle of the unknown voltage can be measured against this reference rotor position.

For the measurement of magnitude with a normal dc potentiometer, all the resistors and the slide wire are replaced by standard non-inductive resistors and slide wire. So that its resistance does not vary with frequency and waveform.

## Procedure for the Measurement :

#### To measure an unknown ac voltage using this potentiometer, first, the meter is standardized. For the standardization, all the three DPDT switches are thrown to position 1 (POS 1), and the current through ammeter (A) for which the D Arsonval galvanometer (G) gives null deflection is noted.

Now, the DPDT switches are thrown to position 2 (POS 2) which connects the rotor terminals of phase-shifting transformer to supply terminals of the potentiometer, vibration galvanometer to detector terminals, and the unknown ac voltage to potentiometer test terminals.

Now, the current through the ammeter is made equal to the current through it when dc supply was connected by varying the standard resistor R and the balance is obtained in the vibration galvanometer by changing the slide wire contact position and the phase shifter's rotor position. Hence, the magnitude and phase of the unknown ac voltage are obtained from the slide wire position and rotor position readings respectively.

## Functions of Transfer Instrument and Phase Shifting Transformer :

### The function of the phase-shifting transformer is,

#### To produce the rotating magnetic field which passes through the air gap between its stator and rotor and induces an emf in the rotor winding. To provide the required phase shifting of the rotor induced emf by adjusting the rotor position. The rotor position can be adjusted by adjusting the rotor angle with respect to the null pointer.

Now, the induced emf in the rotor windings due to two stator windings is given by,
*E*_{1} = KI sinωt cosθ
*E*_{2} = KI sin(ωt + 90) cos(θ + 90)

Therefore, the resultant emf is given by,
*E = E*_{1} + E_{2}
*E = KI [sinωt cosθ + sin(ωt + 90) cos(θ + 90)]*

We know that sin(ωt + 90) = cosωt and cos(θ + 90) = -sinθ.
*∴ E = KI sinωt (ωt - θ)*

From the above, it is clear that the rotor emf has constant amplitude and the phase angle is given by the rotor deflection θ.

*E*

_{1}= KI sinωt cosθ*E*

_{2}= KI sin(ωt + 90) cos(θ + 90)*E = E*

_{1}+ E_{2}*E = KI [sinωt cosθ + sin(ωt + 90) cos(θ + 90)]*

*∴ E = KI sinωt (ωt - θ)*