Measurement of capacitance and loss factor using Schering bridge.

Experiment No.:07

Aim:

To find the value of the unknown capacitance using Schering bridge and thereafter calculate the dissipation factor.

Apparatus Required:

Sl. No.NameQuantity
1Schering Bridge1 nos.
2Single Phase AC Supply230V, 50Hz
3Head Phone1 nos.
4Patch Chordas per required
Table: 7.1

Circuit Diagram:

fig. 7.1
\[\color\green{where,}\] \[\color\red{ R_1 \;= \;}\color\green{a\; non-inductive\; resistor.}\] \[\color\red{R_2 = \;}\color\green{a\; variable\; non-inductive \;resistance}\] \[\color\green{ in\; parallel\; with\; variable\; capacitor\; C_2.}\] \[\color\red{R = }\color\green{a\; series \;resistance\; representing\;}\] \[\color\green{ the\; loss \;in\; the \;capacitor \;}\color\red{C.}\] \[\color\red{C = }\color\green{\;unknown \;Capacitor.}\] \[\color\red{C1 = }\color\green{Standard\; compressed \;air \;capacitor, \;}\color\red{0.01µF}\] \[\color\green{(negligible\; dissipation \;factor)}\] \[\color\red{C2 = }\color\green{a \;Variable\; Capacitor.}\]

Theory:

The Schering bridge is one of the most important and useful circuits available for the measurement of capacitance and dielectric loss. It is widely used both for precision measurements of capacitors on low voltages and for study of insulation and insulating structures at high voltages.

At balance, the head phone should give no sound. The equation at the balance condition can be given

\[\color\red{(R-\dfrac{j}{\omega C}) \Bigg (\dfrac{R_2\dfrac{-j}{\omega C_2}}{R_2-\dfrac{j}{\omega C_2}}\Bigg )=R_1\dfrac{-j}{\omega C_2}}\]

After Simplifying we get,

\[\color\red{C\; =\; C_1\dfrac{R_2}{R_1}}\] \[\color\green{and}\] \[\color\red{R = R_1\dfrac{C_2}{C_1}}\] \[\color\green{thus,\; this\; two\; equations\; when\; satisfied\; together\;}\] \[\color\green{ will\; result\; in \;balance\; of\; the\; bridge.}\] \[\color\green{ Dissipation\; factor\; represented \;by\;}\color\red{ D\;=𝛚CR}\] \[\color\green{here,}\] \[\color\red{𝛚 \;=2πf}\color\green{ ( f\; is\; working\; frequency,\;)}\] \[\color\red{f=\;1kHz}\] \[\color\red{C}\;\color\green{\; = \;unknown \;capacitor}\] \[\color\red{R} \;\color\green{= \;a \;series\; resistance\;}\] \[\color\green{ representing \;the \;loss\;in\; the\; capacitor.}\]

Procedures:

Part 1:

  1. Keep all the dials at zero position.
  2. Connect the AC supply to the bridge supply using patch chords.
  3. Connect the detector, which is a headphone in this experiment.
  4. Connect one of the four ranges of unknown capacitor C, which we are interested to measure.
  5. As C= C1(R2/R1), we can see it doesn’t depend upon C2.
  6. For the first part of experiment R=0, or in other words, we have only the capacitance C in the block.
  7. Now to satisfy R=R1(C2/C), when R=0, C2 is kept to Zero.
  8. Thus to balance the bridge R=0,C2=0, only R1 and R2 to be varied as C1 is a constant.
  9. Find the value of C, by using the expression C=C1(R2/R1).
  10. Repeat the steps to find out the other three unknown values of C.

Part 2:

  1. Take the first unknown capacitor C whose value is now known to us.
  2. Set R1 and R2, so that the bridge comes in null position.
  3. Introduce some resistance R, say 500 from the resistance dial R.
  4. Now some sound will be heard, this is due to R=R1(C2/C1), so R=0 and we have to balance, R=R1(C2/C1)
  5. To balance the bridge adjust the capacitance dial C2 to minimize the sound in the headphone.
  6. Calculate the value of dissipation factor using the formula D= 𝛚CR.
  7. Draw the Phasor diagram after obtaining all the values.

Precaution:

  1. Check all the connections before turning ON the power supply.
  2. Note all readings accurately.

Observation Table:

Sl. No.C1R1R2C=C1(R2/R1)
Unknown Capacitor 1
Unknown Capacitor 2
Unknown Capacitor 3
Unknown Capacitor 4
Table: 7.2
Sl. No.CC1C2R2RD= 𝛚CR
1
2
3
4
Table: 7.3

Conclusion:

To be written by Student.

Previous
Next