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Masja [62]
3 years ago
10

Suppose that the net resistance comes from two resistors in series: R=R1+R2. Assume that you measure each resistor independently

, multiple times in multiple ways, obtaining these mean values and uncertainties: R1={1.234+/-0.007} Ohms and R2={3.142+/-0.014} Ohms. The mean value of the net resistance is (of course): R=4.376 Ohms. Calculate the net uncertainty in this value of R (also in Ohms).
Physics
2 answers:
rewona [7]3 years ago
8 0

Answer:

± (.021 ) ohm

Explanation:

In the addition of two physical quantities , the uncertainties are simply added .

So , net uncertainty in the value of R will be

± (.007 +.014)

=± (.021 ) ohm

jek_recluse [69]3 years ago
5 0

Answer:

\Delta R=0.021\ \Omega

Explanation:

Given:

The resistances in series:

  • R_1=1.234\pm 0.007\ \Omega
  • R_2=3.142\pm0.014\ \Omega
  • Mean value of net resistance, R_m=4.376\ \Omega

<u>We know that the resultant of the resistances in series is given as:</u>

R=R_1+R_2

<em>For the maximum possible deviation in the values being added we take the limits only on one side of the mean values for all the parameters.</em>

R=(1.234+0.007)+(3.142+0.014)\\R=(4.376+0.021)\ \Omega

Therefore the net uncertainty in the value:

\Delta R=0.021\ \Omega

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Let (h/mc) be k

dT/(T - T∞) = -kdt

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In [(T - T∞)/(T₀ - T∞)] = -kt

(T - T∞)/(T₀ - T∞) = e⁻ᵏᵗ

(T - T∞) = (T₀ - T∞)e⁻ᵏᵗ

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(T - 70) = (212 - 70)e⁻ᵏᵗ

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At t = 2 minute, T = 125°F

125 - 70 = 142 e⁻ᵏᵗ

55/142 = e⁻ᵏᵗ

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kt = 0.4742 × 4 = 1.897

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