Half Deflection

To determine the Resistance of the Ballistic Galvanometer Galvanometer as well as the Logarithmic Decrement of the Galvanometer Coil Our aim is to measure the resistance of the ballistic galvanometer and the damping constant of the galvanometer coil (logarithmic decrement) CIRCUIT DIAGRAM

IDENTIFY

!) " long blac# ballist ballistic ic galvanomet galvanometer er standing standing against against the the wall $) " $% elec electr tron onic ic batt batter& er& ') Thre Threee resi resist stan ance ce boes oes R  (ma (ma resistan resistance ce !* !*)+ )+ R ! (ma resistance resistance !*) and R , (ma resistance !*- acting as shunt placed parallel to the galvanometer) which we would need to do the eperiment .) " mic micro ro-a -amm mmet eter er /) " tapping tapping #e& #e& paralle parallell to the galvan galvanome ometer ter 0) " tapping tapping #e& parallel parallel to the resistanc resistancee boes boes R !! 1) " comm commut utat ator or 2) " lamp lamp and scale scale arran arrangem gement ent

Theory:

3f a current i passes in the main circuit and i g  be the current passing through the galvanometer+ we have for the circuit shown in ad4oining fig

 5ow+ 666666($) Therefore+

 5ow if+

then+

 5ow+ from e7uation (.) it is obvious that+ 8hen+ + if (sa&)+ then at

The stead& deflection of the galvanometer is proportional to the current flowing through it+ ie

Therefore+ from the e7uation (.)+ at + the deflection of the galvanometer is eactl& half of the deflection produced when + Thus the value of at which the deflection is getting half is the resistance of the galvanometer The wor#ing formula for log decrement+

8here n9!! Deflection of !st and !!th count of the oscillation

To find the resistance of the Ballistic Galvanoeter

!) Chec# the light spot on the lamp and scale 3t should be on the :ero mar# of the scale $) ;a#e R! 9+ R 9! Ω ') ,witch on the batter& .) The light spot deflects either to the left or to the right and becomes stationar&  5ote down the amount of deflection of the light spot on the scale /) 5ow change R ! to ma#e deflection of the light spot half of the amount as in step .+ and note down the resistance 0) 3ncrease R  in steps of $ Ω and repeat the . < / four times 1) 5ow change the direction of the current b& changing the position of the #e&s in the commutator+ and repeat the steps . to 0 2) Ta#e the mean readings of the value of R ! for half deflection

Table ! = determination of the resistance of the galvanometer

R  (Ω)

Deflection (cm) for R !9Ω

Direct current

Reveres current

R !+ that produce half deflection+ which is 9R g(Ω)

Direct current

Reveres current

T! FIND T"E #A$UE !F T"E $!GARIT"MIC DECREMENT % &

!) ;a#e R 9!Ω and R !9!Ω $) Close tapping #e& > ' and get the maimum deflection+ now release(open) > ' and simultaneousl& ta#e out a #e& from the commutator (in order to brea# the  primar& circuit The light spots start oscillating ') ;easure the deflection for !st throw as well as !!th throw .) Decrease R ! in steps of ! Ω+ and repeat $ < ' four times /) Draw a graph of R !(?-ais) versus λ(@-ais) Table $= Determination of log decrement ( λ )

R !(Ω)

d!

Direct current d!!

! A 2 1 0 /

Ma'i( )ro)ortional error:

8here n9!!+

9!cm+

λ

d!

Reverse current d!!

;ean λ

λ