# Differential equations?

A circuit consisting of a resistance R = 5 ohm and the inductance L = 10H arranged in series is connected at the instant t = 0 to a generator of constant f.e.m equal to f = 50V. Determine the current intensity over time, remembering that f-L * di / dt = R * i

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• 3 months ago

We know at t=0, iL = 0 and we know the time constant τ has units of seconds s AND we know exponents have NO Units. τ = L/R = 10/5 = 2s. After a long time

iL(∞) = 50V/5Ω = 10A

iL(t) = iL(∞)*[1-e^-t/τ)iL(t) = 10(1 - e^-t/2) <<<<<<

• Anonymous
3 months ago

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• 3 months ago

the current will start at zero and increase exponentially to a steady state value of 50/5 = 10 amps.  The τ time constant is L/R = 10/5 = 2 sec.

actual equation isIʟ = (V₀/R)(1–e^(-t/τ))Iʟ = (10)(1–e^(-t/2))