1. DE-SAUTY BRIDGE DEV

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Elinor Nichols
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1 1. DE-SAUTY BRIDGE Object: To determine the capacitance of two capacitors by De-Sauty bridge. Apparatus Used: De-Sauty bridge, connecting wire, Head phone. Formula Used: The following formula is used for the determination of self inductance of coil. P C x C Q Where, Cx: capacitance of unknown capacitor; C : capacitance of unknown capacitor; P and Q: resistances Circuit Diagramme: Observation: 1. C.1μf Fig: Circuit diagram of De-Sauty Bridge. Table for value of P and Q for Ist capacitor Sr. No P(Ω) Perception of sound with Q 5-sound - no sound 7- sound 1-sound - no sound 13- sound 17- sound 18- no sound 19- sound 3- sound 4- no sound 5- sound Q (Ω) (At no sound) C(μf) P C Q x C Mean C(μf).

2 3. Table for value of P and Q for IInd capacitor Sr. No P(Ω) Perception of sound with Q 3- sound 4- no sound 5- sound 7-sound 8- no sound 9- sound 1- sound - no sound 13- sound 15- sound 1- no sound 17- sound Q (Ω) (At no sound) 4. Table for value of P and Q for IIIrd capacitor Sr. No. P(Ω) Perception of sound with Q Q (Ω) (At no sound) Result: sound 3- no sound 4- sound 5-sound - no sound 7- sound 8- sound 9- no sound - sound 1- sound - no sound 13- sound 1. Capacitance of Ist capacitor.μf. Capacitance of IInd capacitor.3μf 3. Capacitance of IIIrd capacitor.4μf C(μf) P C Q x C C(μf) P C Q x C Mean C(μf).3 Mean C(μf) Precaution: 1. Connections should not be loose.. The resistances should be high. 3. If there is found no sound in head phone for a range of Q resistance then total range should be noted and mean of them should be taken for Q at no sound..4

3 .Wavelength of LASER Source with diffraction Object: To determine the wavelength of given LASER source. Apparatus Used: Laser source, meter scale and grating. Formula Used: The following formula is used for the determination the wavelength of given LASER source. ( e + d) θ n λ ( e + d) θ λ n Where, ( e + d) grating element, θ angle of diffraction, n order of diffraction, λ wavelength of LASER source X n θ X n + D Ray Diagram: Observation: 1. number of line per inches of grating (N) grating element ( e + d) 1.7 cm N Table for D and X n Sr.No. D (cm) n X n (cm) Xn Left side Right side Calculation: 1. For D35cm and n1 X θ 1 n X n + D λ cm cm 5 Å 1

4 . For D35cm and n X θ n X n + D λ cm cm 8 Å 3. For D55cm and n1 X θ 3 n X n + D λ cm cm 559 Å 1 4. For D55cm and n X θ 4 n X n + D λ cm cm 737 Å 5. For D75cm and n1 X θ 5 n X n + D λ cm cm 494 Å 1. For D75cm and n X θ n X n + D λ cm cm 7 Å λ Mean 1 + λ + λ3 + λ4 + λ5 + λ λ λ 3 Å Result: The wavelength of given laser source is 3Å Precaution: 1. Laser light and grating should be normal.. Diffracted points should be in a line on screen. 3. Diffracted points in diffraction pattern should have approximately equal/ equal distance from point. central

5 3. G by P. O. Box Object: To determine the galvanometer resistance with Post office Box. Apparatus Used: P. O. Box, cell, rheostat, galvanometer, connecting wires. Formula Used: The following formula is used for the determination of galvanometer resistance. Q G P R Here, G: galvanometer resistance (CD arm resistance of P. O. Box) P: AB arm resistance of P. O. Box Q: BC arm resistance of P. O. Box R: AD arm resistance of P. O. Box Circuit Diagram: or Figure (1) Figure (a) Figure (b) Figure (3)

6 Observation: 1. Table for the value of P, Q and R resistances Sr. No. P (Ω) Q (Ω) Deflection in Galvanometer with R R59Ω, left deflection RΩ, no change in deflection R1Ω, right deflection R58Ω, left deflection R59 to Ω, no change in deflection R1Ω, right deflection R58Ω, left deflection R59 to 1Ω, no change in deflection RΩ, right deflection R58Ω, left deflection R587 to 13Ω, no change in deflection R14Ω, right deflection R584Ω, left deflection R585 to 13Ω, no change in deflection R14Ω, right deflection Calculation: Mean G Ω 5 5 Result: Galvanometer resistance Ω Ω Precaution: 1. Connections should not be loose.. Key K should be always pressed after presg key K 1. R(Ω) G(Ω) (at no change in deflection) If there is found a range of no deflection then total range should be noted and mean of them should be taken for R at no deflection. 4. In P.O. Box the keys should be very tight. 5. Avoid presg keys for large time otherwise cell will be discharged.

7 4. Nodal slide Object: To verify the expression for the focal length of a combination of two lenses. Apparatus Required: Two convex lenses of different focal length and an optical bench with uprights; a lamp of narrow opening, a cross slit screen, nodal slide assembly and a plane mirror Formula Used: The focal length of a combination of two convex lenses is given by, d + F f1 f f1 f where, f 1 and f are focal lengths of two lenses, d is the distance between lenses and F is focal length of combination of two lenses. Figure and Ray Diagramme: Observation: 1. Table for determination of f 1 and f : Lens First second Light incident on the Position of upright (in cm) Cross slit (a) Nodal slide (b) f of lens fa-b (in cm) One face Other face One face Other face Mean of f (in cm) f f.3

8 . Table for determination of f 1 and f : Light Position of upright (in cm) f of lens d Mean of f incident Cross slit Nodal slide fa-b (cm) (in cm) on the (a) (b) (in cm) One face Other face One face Other face One face Other face Calculation: (1) For f 1 1.3cm, f.3cm and dcm d F f1 f f1 f F 1 F cm.17 () For f 1 1.3cm, f.3cm and d8cm d F f1 f f1 f F 1 F cm.18 (3) For f 1 1.3cm, f.3cm and dcm d F f1 f f1 f F 1 F.1.1cm.988 Result: Focal length of Ist lens 1.3cm Focal length of IInd lens.3cm Verification table d (cm) Observed Focal length Calculated Focal length Difference (cm) (cm) (cm) The calculated and experimental values of focal length of the combination of lenses d are approximately equal the formula + is verified. F f1 f f1 f Precaution: 1. All the uprights should be exactly at same height and at same horizontal axis.. The cross slit must be properly illuminated by the intense light coming from lamp. 3. Lenses should be of small aperture to get well defined and sharp image. 4. The mirror employed must be truly plane mirror.

9 5. Conversion of Galvanometer to Voltmeter Object: To convert Weston galvanometer to a voltmeter of voltage range to 3 volts. Apparatus Used: battery, resistance box, galvanometer, voltmeter, rheostat, keys, connecting wires. Formula Used: For the conversion of galvanometer to voltmeter (G V) a high resistance R is connected in series of galvanometer. The value of R is determined by following expression. V R G I g Here, V maximum value of voltage range; G galvanometer resistance I g current for full scale deflection in galvanometer; I g C s N N total number of divisions in galvanometer E C s Current sensitivity of galvanometer or figure of merit; C s n ( R + G) E e.m.f. battery or cell; R resistance involved in galvanometer circuit n deflection in galvanometer on introducing the resistance R in galvanometer circuit. Circuit Diagram: Figure (1) Figure () Observation: 1. Evolt, G7 Ω, N 3. Table for I g Sr. R (Ω) n E No. C s (x - I amp) g C s N mean I g n ( R + G) (x - amp ) (in x - A or µa) Calibration of shunted galvanometer Least count of voltmeter1/.1volt 3 division in galvanometer 3 volt 1 division in galvanometer.1 volt Sr. Galvanometer reading Voltmeter reading Error V -V No. In division In volt ( V ) V ( in volt) (in volts)

10 Calculation: Calculation of C S and I g 1. C s.7 amp 19 (5 + 7) I g amp.8μa. C s.59 amp 1 ( + 7) I g amp 17.7μA 3. C s.1 amp 14 (7 + 7) I g amp.3μa 4. C s.5 amp 1 (8 + 7) I g amp 19.5μA 5. C s.4 amp 11 (9 + 7) I g amp 1.μA Calculation of mean I g I g 13.5 μ A 13 μ A 5 5 Calculation of R R Ω Result: The galvanometer reading and voltmeter reading are approximately same after connecting 484Ω resistance in series of galvanometer thus the resistance required to convert the given galvanometer in to voltmeter of -3volts is 484Ω. Precautions: 1. Resistance in determination of figure of merit should be of high value.. Exact high resistance should be connected in series to galvanometer for conversion to voltmeter. 3. Voltmeter should be connected ug sign convention. 4. Voltmeter used in calibration of shunted galvanometer should be of nearly same range. 5. In calibration process the readings should be noted from zero.

11 . Specific Rotation of sugar Figure Observation 1. Length of polarimeter tube: decimeter value of one div on main scale 1. Least cont of analyzer scale.1 number of div on vernier scale 3. Analyzer reading with water Sr. No. Clockwise Direction (a) For first position Anti-clockwise Direction (a ) a + a θ1 Clockwise Direction (b) For first position Anti-clockwise Direction (b ) b + b θ Mean θ 1.5 Mean θ Mass of sugar 5gm 5. Volume of water ml

12 . Analyzer reading with sugar solution Sr. No. Clockwise Direction (a) For first position Anti-clockwise Direction (a ) a + a θ 1 Clockwise Direction (b) For first position Anti-clockwise Direction (b ) b + b θ Mean θ Mean θ Calculation: Concentration of sugar solution5/ gm/ml.5gm/cc ( θ 1 θ1) + ( θ θ) (73.3.5) + ( ) θ.75 θv cc S lm 5 decimeter. gm Result: At temperature 8 C and at wavelength 55Å Specification rotation of sugar (S) 7.5 cc decimeter. gm Standard value of specification rotation of sugar (S).7 cc decimeter. gm % error in S 1. 5% Precaution:

13 7. Conversion of Galvanometer to Ammeter Object: To convert Weston galvanometer to a ammeter of current range to 1.5 amp. Apparatus Used: battery, resistance box, galvanometer, ammeter, voltmeter, rheostat, keys, connecting wires. Formula Used: For the conversion of galvanometer to ammeter (G A) a low resistance (shunt resistance) S is connected parallel to galvanometer. The value of S is determined by following expression. I g S G I I g Here, I maximum value of current range; G galvanometer resistance I g current for full scale deflection in galvanometer; I g Cs N N total number of divisions in galvanometer E C s Current sensitivity of galvanometer or figure of merit; C s n ( R + G) E e.m.f. battery or cell; R resistance involved in galvanometer circuit n deflection in galvanometer on introducing the resistance R in galvanometer circuit. l length of wire is equivalent to resistance S π l r S ρ Here r is radius of wire, ρ (specific resistance) 1.78x - ohm-cm. Circuit Diagram: Figure (1) Figure () Observation: 1. E volt,. G Ω 3. N 3 4. Table for I g Sr. R (Ω) n E I No. C s (x - amp) g C s N Mean I g n ( R + G) (x - amp ) (in x - A or µa) Least count of screw gauge.1cm. Zero error -.5cm (negative) 7. Diameter of wire (MS +VS x LC)± zero error ( x.1)+.5.9 cm 8. Radius of wire.9/.48 cm 9. Least count of ammeter.5/.5amp 3 division in galvanometer 1.5 amp 1 division in galvanometer.5 amp

14 . Calibration of shunted galvanometer Sr. Galvanometer reading No. In division In amp ( I ) Ammeter reading I ( in amp) Error ( I -I) (in amp) Calculation: Calculation of C S and I g 1. C s 18.8 amp 1 (5 + ) 1 5 I g amp 54. μa. C s 19.4 amp 17 ( + ) 17 3 I g amp 58μA 3. C s 18.9 amp 15 (7 + ) I g amp 57. μa 4. C s 19.1 amp 13 (8 + ) I g amp 573μA 5. C s 18.4 amp 1 (9 + ) I g amp 55μA. C s 19.9 amp ( + ) I g amp 59μA Calculation of mean I g I g 57.3 μ A 57 μ A 57 Ig Calculation of mean S: S G. 8 Ω I I g π r Calculation of l: l S.8 9.7cm 9. 7cm ρ Result: The calibration table indicates that after connecting the wire in parallel combination with galvanometer, the reading in galvanometer and ammeter becomes approximately same. Thus the length of shunt wire required for converting the given galvanometer in to ammeter of range to 1.5 amp is 9.7cm. Precautions: 1. Resistance in determination of figure of merit should be of high value.. Exact length of wire should be connected parallel to galvanometer. 3. Ammeter should be connected ug sign convention. 4. Ammeter used in calibration of shunted galvanometer should be of nearly same range. 5. In calibration process the readings should be noted from zero.

15 8. Newton s Ring Focal length of plano-convex lens is given by ( μ 1) f ( 1) R R μ 1 R 1 ( μ 1) (1.5 1).5 1 f R R R R f R Here f is focal length of plano-convex lens. Figure Observation: 1. Value of one division on main scale1/.5 cm. Total number of division on Vernier scale5 3. Least count of microscope.5/5.1cm

16 4. Table for diameter of rings Sr. No. LHS reading (cm) RHS reading (cm) D L R No. Of MS VS Total MS VS fringes (cm) (div) (L) (cm) (div) Total (cm) (cm ) Focal length of lens 13 cm Calculation: Radius of curvaturerf/13/5cm Mean of D Dn+ p n (for p). 913 cm 3 3 (R) Dn+ p Dn λ cm 4 pr λ 5853 cm 5853 Å Result : The wavelength of sodium light 5853 Å Precaution: Sodium light has two wavelengths 589 Å and 589 Å thus, Standard value for wavelength of sodium light 5893 Å % error in wavelength. 8 % D D D n+ p n (cm ) for p

17 9. Variation of magnetic field at axis of circular coil Object: To study the variation of magnetic field with the distance along the axis of current carrying circular coil ug Stewart and Gee s apparatus. Apparatus required: Stewart and Gee s type tangent galvanometer, a battery, a rheostat, an ammeter, a one way key, a reverg key (commutator), connecting wires. Formula: If a current carrying coil is place in y-z plane then its axis will be x-axis. The magnetic field along the axis of coil is given by, μ NI a B (1) 3 / ( a + x ) Where, μ ( 4π 7 ) is the vacuum permeability, N is the number of turns of the field coil, I is the current in the wire, in amperes, a is the radius of the coil in meters, and x is the axial distance in meters from the center of the coil. If θ is the deflection produced in magnetometer at a certain position on the axis of coil then magnetic field at that point will be, B H tanθ () The equations (1) and () implies that the graph between x and tanθ will give the variation of magnetic field at the axis of circular coil. Figure and Circuit Diagram Observations. 1. Least count of the magnetometer 1. Current I 1 amp 3. Table A: Deflection in magnetometer along +axis of coil. Sr. Distance of needle Deflection on East arm No from centre of Current in one Current in reverse Mean centre, x (cm) direction direction θ tanθ θ 1 θ θ 3 θ 4 in deg

18 4. Table B: Deflection in magnetometer along -axis of coil. Sr. Distance of needle Deflection on East arm No from centre of Current in one Current in reverse Mean centre, x (cm) direction direction θ tanθ θ 1 θ θ 3 θ 4 in deg Plot in x and tanθ: Result: With help of the graph between tan θ and x, following points can be concluded. 1. The intensity of magnetic field has maximum at the centre and goes on decreag as we move away from the centre of the coil towards right or left.. The point on the both side of graph where curve becomes convex to concave (i.e. the curve changes its nature) are called the point of inflection. The distance between the two points of inflexion is equal to the radius of the circular coil. 3. The radius of coil distance between points of inflection1cm Precautions: 1. There should be no magnet, magnetic substances and current carrying conductor near the apparatus.. The plane of the coil should be set in the magnetic medium. 3. The current should remain constant and should be reversed for each observation.

19 . Resolving Power of telescope Figure: Observation: 1. Wavelength of light source 55x -8 cm. Pitch5/.5mm.5 cm Total number of division on circular scale5 Least count of micrometer.5/5.1cm 3. Table for width of rectangular slit for just resolve position: Sr. Distance Micrometer reading (cm) Width of slit No. D (cm) When two slits merge and appear one When both slits completely disappear ax-y (cm) MS (cm) VS (div) Total (x) MS (cm) VS (div) Total (y)

20 4. Pitch1/.1 cm Total number of division on circular scale Least count of micrometer.1/.1cm 5. Table for width of rectangular slit for just resolve position: Sr. Microscope reading (cm) Distance No. For left slit For right slit between slits MS (cm) VS (div) Total (X) MS (cm) VS (div) Total (Y) dx-y (cm) Calculation: Mean d.15 cm 1. For D cm a λ D 41. d For D cm a λ D 79. d For D14 cm a λ D d For D1 cm a λ D d Result: Obtained theoretical and practical resolving powers of the telescope are shown in table- D (cm) a D λ d Since theoretical and practical resolving powers of the telescope are approximately same thus the expression for resolving powers of the telescope is verified. Precaution:

21 11. ANDERSON BRIDGE Object: To determine the self inductance of a coil by Anderson bridge. Apparatus Used: Anderson bridge, connecting wires, Head phone. Formula Used: The following formula is used for the determination of self inductance of coil. Q L C RQ + rr 1 + P Q S Since, S R ; thus L C P RQ + rr 1 + R L C[ RQ + r{ R + S} ] If PQ then SR; Hence, L C[ RQ + rr] L RC[ Q + r] Where symbols have their usual meaning as shown in figure. Circuit Diagram: Fig (A): Bridge with DC source and galvanometer Fig (B): Bridge with AC source and Head Phone Observation:. P Ω 3. Q Ω 4. Table for value of R and r when C.1 μf Sr.No. Inductor R(Ω) for zero deflection in Galvanometer (G) under DC balancing rω) for no sound in Head phone (H) under AC balancing L(mH) (Inductance) [ r] L RC Q + 1. First 54 3 L Second 8 54 L Third L

22 5. Table for value of R and r when C. μf Sr.No. Inductor R(Ω) for zero deflection in Galvanometer (G) under DC balancing r(ω) for no sound in Head phone (H) under AC balancing 1. First Second Third 4 59 Calculation: A. For C.1μf [ + 3] L mh [ + 54] L 8.1 mh [ + 54] L(mH) (Inductance) [ r] L RC Q + L L 94. L 48.5 L mh B. For C.μf [ + 17] L 54. mh [ + 53] L 8. mh [ + 9] L 4. mh Result: L Inductance of Ist inductor 1 + L mh L Inductance of IInd inductor + L mh L3 + L Inductance of IIIrd inductor mH Precaution: 1. To avoid inductive effect short straight wires should be used.. Movement in galvanometer should be free. 3. The resistances should be high and non-inductive. 3

23 1. μ by spectrometer Figure: Figure1: For angle of prism Figure: For angle of deviation Observation: Value of one division on main scale 3 3 minute. Number of division on Vernier Value of one div on main scale 3. Least count of spectrometer Number of division on vernier scale second 4. Table for angle of prism Sr. No. 1.. Vernier Telescope reading for reflection A A From first face From second face (a~b) MSR VSR Total MSR VSR Total (a) (div) (b) V x x V x x V x x V 48 3 x x Mean of A 3

24 5. Table for minimum angle of deviation (δm) Sr. No. Colour 1. Voilet. Yellow 3. Red Calculation: μv Ver -nier Telescope reading for reflection At minimum deviation Direct δm (a~b) MSR VSR Total MSR VSR Total (a) (div) (b) V 1 3 3x x V 3 3x x V x x V 4 3 5x x V x x V 3 37x x A + δ V A μ V μy ( ) ( 3 15 ) A + δ Y A μ Y μ R ( 51 3 ) ( 3 15 ) A + δ R A 3 3 μ R ( 5 53 ) ( 3 15 ) Result: μ V μ Y μ R Precaution: Mean δm

25 13. LCR-Circuits Object: To determine the impedance of LCR circuit. Apparatus Used: resistance, inductor coil, capacitor, connecting wires, a.c. voltmeter, mili-ammeter, low voltage a.c. source. Formula Used: The following formula is used for the determination of impedance of LCR circuit. Z R + ( X ) L X C Where, Z : impedance of LCR circuit, X : Inductive reactance, Circuit Diagram: Observation: L R : resistance X : Capacitive reactance dvr dvr dvc R, X L and X C di R di L di C V R, V L and V C are the voltage across R, L and C respectively. I R, I L and I C are the currents through R, L and C respectively. 1. Least count of voltmeter. volts. Least count of mili-ammeter 5 ma 3. Table for value of voltage and current R-Circuit L-Circuit C-Circuit LCR-Circuit Sr.No. V R (volt) I R (ma) V L (volt) I L (ma) V C (volt) I C (ma) V (volt) I (ma) C

26 Graph- Fig.1 Fig. Fig.3

Calculation: From Fig.1, From Fig., From Fig.3, From Fig.4, AB.8 R tan θ BC 3 4 ab.8 X L tan θ bc 3 MN X C tan θ NO Fig.4 1. 3 3 PQ 1.9.7 Z tan θ QS 3 (5 3) 8 Ω 4 8 8Ω 4Ω 3 44.

27 Calculation: From Fig.1, From Fig., From Fig.3, From Fig.4, AB.8 R tan θ BC 3 4 ab.8 X L tan θ bc 3 MN X C tan θ NO Fig PQ Z tan θ QS 3 (5 3) 8 Ω 4 8 8Ω 4Ω Ω 7 ( ) + ( 8 4) Ω Z R + X L X C 7 Result: Precaution: 1. R Ω X L 8 Ω X C 4 Ω. Z graph Ω Z calculated 44.7 Ω 1. Connections should be tight.. Variation in voltage should be in slow manner. 3. Reading of voltage and current should be started with zero.

28 14. λ by grating Figure: Figure A: normal incidence Figure: diffraction through grating Observation: Value of one division on main scale 3 3 minute 1.. Number of division on Vernier Value of one div on main scale 3. Least count of spectrometer Number of division on vernier scale second 4. Number of lines per inch15, 5. Grating element.54/15 1.9x -4 cm. Reading of Vernier for direct image: Reading of Vernier after rotating telescope by

29 8. Reading of Vernier when reflected image is obtained at cross wire Reading of Vernier after rotating prism table by Table for angle of 1st order diffraction Telescope reading for reflection Sr. No. Colour 1. Violet. Blue 3. Yellow 4. Red Ver At minimum deviation Direct θ -nier Total VSR Total (a~b) MSR VSR MSR (a) (div) (b) V x x V x x V x x3 3 3 V 18 3 x x V x x V 3 1x x V x x V 4 1x x Calculation: For diffraction through grating, When n1 then ( a + b) θ nλ λ ( a + b) θ 3 3. For violet colour, θ v 15 λv ( a + b) θv λv 4374 cm 4374 Å For violet colour, θ G λg ( a + b) θg λg 593 cm 593Å For violet colour, θ Y 45 λy ( a + b) θy λy 5988 cm 5988 Å For violet colour, θ R 45 λ R ( a + b) θr λ R 535 cm 535Å Precaution: Result: The obtained wavelengths of different colours are as followsλ v 4374 Å λ G 593Å λ Y 5988Å λ R 535 Å Mean θ

Helmholtz Galvanometer

Helmholtz Galvanometer To plot a graph showing the variation of magnetic field with distance along the axis of a Helmholtz galvanometer and determine the reduction factor k. B.Tech-I, Physics Laboratory