# Losing Heat

Calculus Level 1

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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