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4 years ago

A steel railroad track has a length of 31 m

Physics

1 answer:

Bess [88]4 years ago

7 0

Answer:

DL = 0.0105 [m] = 10.57 [mm]

Explanation:

To solve this problem, we use the following equation that involves length changes depending on temperature changes.

$DL=\alpha *DT*L$

where:

DL = length change

α = thermal expansion coefficient = 11 * 10^(-6) [1/°C]

DT = temperature change = (37-6) = 31 [°C]

L = nominal or initial length = 31 [m]

DL = 11 * 10^(-6) * 31 * 31

DL = 0.0105 [m] = 10.57 [mm]

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What is the time constant of a series circuit where the capacitor is 0.330μF and the resistor is 10Ω ?

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Answer:

$\tau=3.3*10^{-6}s$

Explanation:

Take at look to the picture I attached you, using Kirchhoff's current law we get:

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This is a separable first order differential equation, let's solve it step by step:

Express the equation this way:

$\frac{dV}{V}=-\frac{1}{RC}dt$

integrate both sides, the left side will be integrated from an initial voltage v to a final voltage V, and the right side from an initial time 0 to a final time t:

$\int\limits^V_v {\frac{dV}{V} } =-\int\limits^t_0 {\frac{1}{RC} } \, dt$

Evaluating the integrals:

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natural logarithm to both sides in order to isolate V:

$V(t)=ve^{-\frac{t}{RC} }$

Where the term RC is called time constant and is given by:

$\tau=R*C=10*(0.330*10^{-6})=3.3*10^{-6}s$

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