Potential dividers

Jason  Wen  

Physics  

March  31st,  2015  

Potential  dividers   Prelude   This  experiment  assumes  that  the  voltmeter  has  infinite  resistance  and  ammeter   has  negligible  resistance.   The  spread  in  values  of  Vout  for  each  value  of  R1  is  known  as  random  error.   There   is   a   zero-­‐offset   error   if   the   voltmeter   measured   a   p.d.   of   0.20V   when   the   battery  was  disconnected  due  to  lack  of  calibration.   8   different   values   of   R1   were   used   in   the   experiment,   which   is   enough   to   see   a   pattern  between  the  variables.   The   uncertainty   in   Vout   for   the   largest   value   of   R1   was   ±0.07   considering   that   !.!"

there   is   additional   uncertainty   in   the   resistors,   and   is   =!"#(!

!"# )

=±2.5%   as   in  

percentage  of  the  mean  value  of  Vout.  

Raw  data   R1/Ω   R2/Ω   Vin/V   Vout/V   5  ±  0.5   15  ±  0.5   8.50  ±  0.4   6.75  ±  0.90   10  ±  0.5   15  ±  0.5   8.50  ±  0.4   5.50  ±  0.90   15  ±  0.5   15  ±  0.5   8.75  ±  0.4   5.00  ±  0.90   150  ±  5   15  ±  0.5   9.00  ±  0.4   1.25  ±  0.20   300  ±  50   15  ±  0.5   9.00  ±  0.4   0.70  ±  0.20   1200  ±  50   15  ±  0.5   9.00  ±  0.4   0.20  ±  0.20   4700  ±  50   15  ±  0.5   9.25  ±  0.4   2.00*±  0.20   10000  ±  500   15  ±  0.5   9.25  ±  0.4   0.25  ±  0.20   Note   that   the   uncertainty   of   R1   and   Vout   vary,   since   different   values   of   resistors   and  different  scale  precisions  of  the  voltmeter  were  applied.  

Processed  data   (R1+R2)-­‐1/Ω-­‐1   0.050   0.040   0.033   0.006   0.003   0.001   0.000   0.000  

Vout/V   6.75  ±  0.90   5.50  ±  0.90   5.00  ±  0.90   1.25  ±  0.20   0.70  ±  0.20   0.20  ±  0.20   2.00*±  0.20   0.25  ±  0.20  

Since  it  is  suggested  that   𝑉!"# = 𝑉!" !

!!

! !!!

,  thus  Vout  is  plotted  against  (R1+R2)-­‐1.  

Jason  Wen  

Physics  

March  31st,  2015  

Conclusion   Voltage  output  (Vout)  agiansts  inverse  of  total   resistance  ((R1+R2)-­‐1) 9.00     8.00     7.00     6.00    

Vout/V

5.00     y  =  132.49x  +  0.2806   R²  =  0.99607 Maximum  gradient  =  149.36 Minimum  gradient  =  115.61

4.00     3.00     2.00     1.00     0.00     0.000    

0.010    

0.020    

0.030     0.040     (R1+R2)-­‐1  /Ω-­‐1

0.050    

0.060    

The   gradient   of   the   graph  (𝑉!" 𝑅! )   represents   the   product   of   voltage   input   and   resistance   of   resistor   two.   The   graph   does   support   the   suggest   equation   as   indicated   by   the   R2   value  ≈ 1,   meaning   that   there   is   a   very   strong   correlation   between  Vout  and  (R1+R2)-­‐1.   Theoretical  value  of   𝑉!" 𝑅! :   𝐴𝑣𝑔 𝑉!" ×𝑅! = 8.91×15 = 134𝑉𝛺   Uncertainty  of  gradient  compare  to  theoretical:  

Jason  Wen  

Physics  

March  31st,  2015  

∆𝑚 134 − 132 = = ±1.5%   𝑚 134

Evaluation   Although   the   R2   value   and   low   uncertainty   of   gradient   showed   the   experiment   has   obtained   a   reliable   result,   the   range   between   maximum   and   minimum   gradients   is   relatively   large   (

!"#!!!" !"#

= ±25%)   showing   an   unreliable   result.  

Overall,  the  results  obtained  are  relatively  reliable  considering  the  experiment  as   a  whole.   Reliability   could   be   increase   by   having   more   trails   and   greater   number   of   increments.   Precision   could   be   increase   by   replacing   analogue   meters   with   digital  meters   The  instruction  of  “switch  off  or  disconnect  the  battery  between  readings”  was  to   avoid   heating   effect,   which   will   vary   the   resistance   of   other   components   in   the   circuit  such  as  wire  and  resistor  two.