Question

Suppose you need your silicon circuit element to run continuously for 3 minutes before it shuts off long enough to cool back down to its initial temperature. If the circuit element can withstand a temperature change of 5.1 ∘C without being damaged, what is the maximum rate at which energy can be added to the circuit element?

Answer 1

The maximum rate at which energy can be added to the circuit element mathematically given as

$MER=5.044 \times 10^{-4} \mathrm{~J} / \mathrm{sec}$

What is the maximum rate at which energy can be added to the circuit element?

Generally, the equation for P is  mathematically given as

$P=\ln s \frac{\Delta T}{\Delta t}$

Therefore

$Rate\ of\ Change\ of\ Temp =\frac{p}{lnS}$

$\frac{p}{lnS}=\frac{7.4 \times 10^{-3}}{23 \times 10^{-6} \times 705}$

$\frac{p}{lnS}=0.456^{\circ \mathrm{c}} / \mathrm{sec}$

Max temp Change

$MaxT=5.6^{\circ} \mathrm{C}$

$\text { time }=3 \times 60$

t=180s

In conclusion, Max Energy Rate

$MER =23 \times 10^{-6} \times \frac{301 \times 5.6}{180}$

$MER=5.044 \times 10^{-4} \mathrm{~J} / \mathrm{sec}$

Read more about  Energy

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