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# Related Rates

How does pressure change in a combustion engine? How fast does the water level rise when filling a pool? Calculus quantifies the impact of change on areas, angles, distances, temperatures, and more.

The amount of heat dissipated through a resistor of resistance \(R\) through a circuit with voltage \(V\) for \(t\) seconds is approximated by the formula \(H = \displaystyle\frac{V^2t}{R}\).

After the circuit has been on for 5 seconds, the resistor has been heating up and its resistance is \(10 \Omega\) while increasing at a rate of \(1 \Omega / \text{s}\). What is the rate (in J/s) that heat is being dissipated through this resistor at this moment if the circuit is operating at a constant voltage of \(V = 12\)?

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