Theory of Intelligence
11TH•Mathematics•Sequences And Series•Question 14

Overview

In an integrated circuit with an initial current of 1080 mA, the temperature in the components decreases from 20% to 17% to 14%. Assuming that each temperature decrease is caused by a decrease in the initial current, what is the value of the current at fourth measurement?

Temperatures: 20%, 17%, 14%, … form an A.P. with common difference ( -3% ).

Fourth measurement temperature = ( 20 - 3\times 3 = 11% ).

Assuming current is proportional to the temperature percentage and the initial current 1080 mA corresponds to the first measurement (20%):

[ \frac{1080}{20} = 54 \implies \text{current at 11%} = 11\times 54 = 594,\text{mA}. ]

Alternatively, the successive currents themselves form an A.P.: [ 1080,; 1080\times\frac{17}{20}=918,; 918\times\frac{14}{17}=756,; 756\times\frac{11}{14}=594. ]

Answer: 594 mA

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