Question

Power can be determine by using three possible ways and there are P = I x V,
P = V² / R and P = I² X R. This experiment will use 2 k resistor which having
resistance accuracy limitation of ±0.25%. The measurement was taken by using
voltmeter with the accuracy limitation within ±0.55% of the maximum range, 10 V to
measure the voltage across the resistor and an ammeter having accuracy limitation
within ±0.40% of maximum range, l0mA to measure the current passing through the
resistor. The voltmeter reads 7.5 V and the ammeter reads 7.5 mA. From these three
equations, which one is the most accurate and justifies the answer.

Answer 1

Answer:- When we use the first equation i.e P = V x I then,
uncertainity in power = 7.5 x 0.0075 x (0.55² + 0.4²)^0.5
= 0.0120322 %

When we use second equation i.e P = V²/R then,
uncertainity in power = (7.5 x 7.5 / 2000) x (2x(0.55²) +0.25²)^0.5
= 0.0125312 %


When we use second equation i.e P = I² x R then,
uncertainity in power = 0.0075 x 0.0075 x 2000 x (2 x (0.4²) + 0.25²)^0.5
   = 0.0164594 %


Thus using the first equation will give more accurate answer.