An alternating current flows through a resistor

PHYSICS · Subjective · Fermi University Physics · Mathematical Methods for Physics · Electricity, Magnetism & Electromagnetism · Calculus of change and accumulation

Mathematical Methods for Physics, Ch The derivative as a physical instrument

Problem

An alternating current I(t)=I0sin⁡(ωt)I(t) = I_0\sin(\omega t) flows through a resistor R=50 ΩR = 50\,\Omega, with I0=2.0 AI_0 = 2.0\,\mathrm{A} and ω=100π rad s−1\omega = 100\pi\,\mathrm{rad\,s^{-1}}. The instantaneous power dissipated is P(t)=I(t)2RP(t) = I(t)^2 R. Find dP/dt\mathrm{d}P/\mathrm{d}t at t=2.0×10−3 st = 2.0\times10^{-3}\,\mathrm{s}, taking RR to be constant (unaffected by heating).

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