Measurement of low resistance using Kelvin Double Bridge.

Experiment No.: 04

Objective:

To measure the value of low resistance.

Apparatus Required:

Sl. No.Name (Specification)Quantity
1Kelvin’s Portable Bridge1 nos.
2Four terminal Resistance (75A, 75mV)1 nos.
3Connecting Wire1 nos.
Table:4.1

Features of the Bridge:

a. The source of the bridge is 4V, 2A.

b. The bridge has a main dial. There are 10 coils of 0.1 Ω each.

c. The bridge is provided with a slide wire. The resistance of the slide wire is 0.1Ω. Each main division is equal to 0.001Ω and each sub-division is equal to 0.0005Ω. The reading of the left of zero is to be subtracted and that to the right of the zero is to be added to main dial reading.

d. In this bridge a range multiplier switch is there which furnishes five ranges of X0.01, X0.1, X1, X10 and X100.

e. The value of the unknown resistance R is found out by sum of main dial and slide wire reading, multiplied by range used.

f. The range of resistance that can be measured with the help of the bridge is 0.00001Ω to 110Ω.

Circuit Diagram:

Theory:

Kelvin’s double bridge is used to measure a small resistance. Small resistance falls in the category of resistance less than 1 Ω. The Wheatstone bridge does not take into account the contact or the lead resistance and hence error is considerable. Four terminal resistors have two current lead-in terminals and two potential terminals across which the resistance equals the marked nominal value. This because, the current must enter and leave the resistor in a fashion that there is same or equivalent distribution of current density between the particular equipotent surfaces used to define the resistance. The additional points also eliminate any contact resistance at the current lead-in terminals. Kelvin’s double bridge possess two set of ratio arms. The ratio P/Q and p/q must be equal so that the contact resistance can be avoided. For a particular value of P/Q (0.01,0.1, 1, 10) multiplier the value of standard resistance S is adjusted such that the galvanometer gives no deflection.

After solving the bridge in balanced condition, unknown resistance R comes out to be,

\[\color\red{R=\dfrac{P}{Q}\times{S}+\dfrac{qr}{p+q}\times(\dfrac{P}{Q}-\dfrac{p}{q})}\] \[\color\green{where:}\] \[\color\magenta{ P\; and\; Q \;are\; the\; outer\; ratio \;arms }\] \[\color\magenta{and \;p \;and\; q \;are\; the\; inner\; ratio\; arms}\] \[\color\magenta{ and\; r\; is\; the\; parasitic\; resistance}\] \[\color\magenta{ which\;we\; want\; to\; exclude.}\] \[\color\green{So \;it \;can\; be\; easily\; understood\; if}\] \[\color\red{\dfrac{P}{Q}=\dfrac{p}{q}}\] \[\color\green{then}\] \[\color\red{R\;=\;\dfrac{P}{Q}\times{S}}\]

Thus the parasitic resistance r gets eliminated.

Procedures:

  1. Connect the four terminal resistance to the respective points in the kelvin’s bridge setup.
  2. Internal galvanometer is already present in the setup. Connect an external galvanometer for greater sensitivity.
  3. Keep the multiplier (P/Q) at a particular ratio and vary the standard resistance S so that the galvanometer gives zero deflection.
  4. When you are starting the balance use the internal galvanometer. The push button in the setup enables to complete the path of the galvanometer and hence current flows through it. Do not push the ‘push button’ for indefinite time as this may damage the galvanometer.
  5. When the bridge is balanced find out the unknown resistance by using the expression,
\[\color\red{R\;=\dfrac{P}{Q}\times{S}}\]

6. If balance is not obtained then change the multiplier and try to achieve the balance.

Precaution:

  1. Don’t push the push button for prolonged state. The push button must be pressed momentarily to check if the pointer of the galvanometer is deflecting or not.

Observation Table:

Sl. No.Multiplier (P/Q)SR=(P/Q)*S
1
2
3
4
5
Table: 4.2

the value of the unknown resistance can be found out by finding the arithmetic mean of the R for different multipliers.

Conclusion:

To be written by Student.

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