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MathCalculus

Related Rates Calculus: Current Change as Voltage Falls and Resistance Rises

Find the instantaneous current rate when voltage falls and resistance rises.

Question

In a simple circuit V=IRV=IR, with VV in volts, II in amperes, and RR in ohms. When R=400 ΩR=400\ \Omega and I=0.04 AI=0.04\ \mathrm A, voltage is decreasing at 0.03 V/s0.03\ \mathrm{V/s} and resistance is increasing at 0.03 Ω/s0.03\ \Omega/\mathrm s. Find the instantaneous rate of change of current in amperes per second.

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Evidence boundary

The rates are instantaneous at the same moment as R = 400 Ω and I = 0.04 A. Decreasing voltage means −0.03 V/s; increasing resistance means +0.03 Ω/s. This uses the 2024 publisher PDF version.