- The Determination Of Resistance And Resistivity Aims A To Acquaint You With An Important Bridge Circuit The Wheatsto 1 (340.1 KiB) Viewed 52 times
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- The Determination Of Resistance And Resistivity Aims A To Acquaint You With An Important Bridge Circuit The Wheatsto 3 (423.93 KiB) Viewed 52 times
- The Determination Of Resistance And Resistivity Aims A To Acquaint You With An Important Bridge Circuit The Wheatsto 4 (50.42 KiB) Viewed 52 times
- The Determination Of Resistance And Resistivity Aims A To Acquaint You With An Important Bridge Circuit The Wheatsto 5 (331.97 KiB) Viewed 52 times
- The Determination Of Resistance And Resistivity Aims A To Acquaint You With An Important Bridge Circuit The Wheatsto 6 (185.69 KiB) Viewed 52 times
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The balance condition is given by PS E3.2 Q X Proof i. At balance no current flows between b and d, and so the current (11) in S and X must be the same, as must the current (12) in P and Q. ii. b and d must be at the same potential, since no current flows through bd. iii. Then Vab = Vad and Vbc = Vdc, and so I, S = 1,P and I,X =1,2 Dividing gives equation (E3.2). (iii) The slide-wire bridge The slide-wire bridge is a Wheatstone bridge in which the resistances P and Q in figure (E3.1) are replaced by a uniform resistance wire, and S is replaced by a known (standard) resistance. A sliding contact can be Р moved along the wire, altering the ratio until balance is found. S (or X) X (or S) 2/4 a с 42- FIGURE E(3.2) d -If the slide-wire has a uniform cross-sectional area Asw and resistivity Psw, show that a R. _ų Rac 2 E3.3 Where l, and l2 are the lengths ad and dc. If S is a known and X an unknown resistance, write down the equation connecting X, S, 11 and 12. E3.4
Method Find the unknown resistance of a wire with length 1.0m Procedure: 1. The arrangement of the apparatus should be as shown in the circuit diagram. 2. The wire whose resistance is to be determined should be connected in the right gap between C and B without any formation of loops. 3. The resistance box should be connected in the left gap between A and B. 4. All the other connections should be as shown in the circuit diagram. 5. Plug the key K in place of 2-ohm resistance in the resistance box. 6. The jockey should be first touched gently to the left end and then to the right end of the bridge. 7. The deflections in the galvanometer should be in opposite directions and if it is in one direction then the circuit connections are not correct. Note the galvanometer deflection. 8. Let D be the null point where the jockey is touching the wire. The movement of the jokey should be gentle from left to the right of the galvanometer. 9. Take a standard resistance (S) value from the resistance box should be taken such that when the jockey is nearly in the middle of the wire, there shouldn't be any deflection. 10. Note the position of D to know the length of AD = 1. 11. Five sets of observations should be taken by changing the value of standard resistance S. 12. Record the observations in a tabular form. 13. Stretch the resistance wire to find its length using a meter scale. 14. Using screw gauge measure the diameter of the wire at four different places keeping it in a mutually perpendicular direction. 15. Record the observations in the table. Results Standard Resistance S = 2,00 22 X XL Observations from the conducted experiment S on: Length(L) (m) 1 (m) left 0,90 0,512 right 0,90 0,486 left 0,80 0,541 right 0,80 0,456 left 0.70 0,575 right 0.70 0,421 12 (m) 0,488 0,514 0,459 0,544 0,425 0,579 Calculate the mean resistance from the table. X Plot a graph of X against L and from it determine L Find the mean resistance per unit length = 3/4
Radius of the resistance wire d = 0.43 mm Mean radius r = A = nr2 Conclusion X Calculate the resistivity of the wire using equation (E3.1) in the form p= A. L Wire used ............. Resistivity p =
To find the resistance of the wire S.No Standard resistance (Resistance from box) (S) Balance length 1 Remaining length (100 – (cm) 11 = 12) (cm) Unknown resistance X 11 süz (1) 1 1 75.3 2 2 61.4 3 3 52.0 4 4 44.9 5 5 39.0 1) To find diameter of the wire Fler photo d = 0.43 mm Mean radius r = 2 Α = πη2 Calculate Resistivity p = (R/L) A am Note: here R is unknown resistance X
EXPERIMENT 3 THE DETERMINATION OF RESISTANCE AND RESISTIVITY . AIMS: Introduce theory and understand the concepts behind Wheatstone Bridge Circuit. Determine the resistance for various lengths of current conducting wire using a slide-wire bridge. Determine the resistance per unit length and hence the specific resistivity of the wire used. . . Resistance and Resistivity: The resistance (R) of a wire with length (L) and uniform cross-section area (A) is proportional to the length (L) of the wire and inversely proportional to the cross-sectional area. R= p (L/A) → Eq.1 where p is the resistivity and is material specific and is co istant to the specific material at a given temperature. = Eq.1 can be rearranged to : p = (R/L) A- ----------- → Eq. 2 (where R/L is resistance per unit length of the wire) Kirchhoff's First Law and Second Law: 1. Current flowing into a circuit junction must be equal to current flowing out of it. (This is a consequence of charge conservation). 2. The sum of all voltages around any closed loop circuit must equal zero. This is a consequence of charge conservation and conservation of energy
Wheatstone Bridge B . . Here four resistors P,Q,R and S are connected to form the network ABCD. The terminals A and C are connected to a battery, and the terminal B and D are are connected to Galvanometer through keys K, and Krespectively. In the balancing condition, there is no deflection on the galvanometer. Then their resistances ratios are P/Q = R/S → Eq.3 S ------- 12 12 D E K Slide-Wire Bridge Materials Required: 1. Meter bridge 2. Battery eliminator 3. Galvanometer 4. Resistance box 5. Jockey 6. One-way key 7. A resistance wire 8. Screw gauge 9. Ruler 10. Connecting wires 11. Rheostat
. Meter bridge Apparatus: The meter bridge, consists of a one-meter long wire of uniform cross-sectional area, fixed on a wooden block. A scale is attached to the block. Two gaps (between AB and BC) are formed on it by using thick metal strips in order to make the Wheat stone's bridge. The terminal B between the gaps is used to connect galvanometer and jockey. A resistance wire of unknown resistance X is introduced in gap between BC. A resistance box with standard resistance S is introduced in the gap between AB. One end of the galvanometer is connected to terminal D and its other end is connected to a jockey. As the jockey slides over the wire AC, it shows zero deflection at the balancing point (null point) . . . Cell or battery eliminator 6) Battery eliminator or leclanche cell Resistance Box If balancing length is 17 (1) and remaining length is 12(100- Then according to Wheatstone's Principle X/S = 11/12 (from Eq.3) X = ? Unknow wire B Now the unknown resistance can be calculated as X = S (14/12 -→ Eq.4 R -------- 10 20 30 40 50 (100-1) 60 70 80 90 100 ilul D А C Bridge wire Scale Galvanometer
To find the resistance of the wire S.No Standard resistance (Resistance from box) (S) Balance length 1 Remaining length (100 - (cm) 11 = 12) (cm) Unknown resistance X 11 = ESTż (1) 1 1 75.3 2 2. 61.4 3 3 52.0 4 4 44.9 5 5 39.0 » To find diameter of the wire d = 0.43 mm Mean radius r = A = fr2 Bo 0.01mm 0-25 Calculate Resistivity p = (R/L) A Ω m Note: here R is unknown resistance X In this experiment we have learned how to determine resistance and resistivity of unknown wire by using Slide-Wire Bi