Physics · Current Electricity
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The power loss 𝑃 in a resistor is calculated using the formula: 𝑃 =𝑉2/R
The uncertainty in the potential difference 𝑉 is 3% and the uncertainty in the resistance 𝑅 is 2%. What is the uncertainty in 𝑃?
- A
4%
- B
7%
- C
8%
- D
11%
•The fractional error in V would be
3×2=6
•The fractional error in R would be
2
•So the fractional error of power would be equal to the sum of the fractional errors of both potential difference and resistance;
6+3=8
•NOTE= The given % error is multiplied by the power as in case of potential difference.
4% is incorrect. It assumes incorrect calculations for uncertainties in V and R. Revisit how uncertainties are combined.
7% is incorrect. While it may seem plausible, it doesn't account for the proper addition of uncertainties in quadrature. Recalculate using the correct method.
8% is correct. The uncertainty in power is calculated by adding the percentage uncertainties of V and R considering the power relation V2/R. Thus, 2(3%) + 2% = 8%.
11% is incorrect. This option overestimates the uncertainty. Review the correct way to combine uncertainties for quantities involving powers.
Tagged under Physics · Current Electricity · 2018