atimia:

if circuit theory tells us that V= RI + L(dI/dt)

prove that I= V/R + Ae^[-(R/L)*t]

SOMEONE HELP ME PLEASE

I kept going into physics mode and thinking V was voltage lol. Then I realised it WAS ACTUALLY VOLTAGE AND HIT MYSELF IN THE HEAD

V = RI + L(dI/dt)

L(dI/dt) = V - RI

dI/dt = (V-RI)/L

dt/dI = L/(V-RI)

dt/dI = -(L/R)*[-R/(V-RI)]

t = -(L/R) * loge (V-RI) + c

loge (V-RI) = -tR/L + cR/L

loge (V-RI) = R/L (c - t)

e^[R/L(c-t)] = V-RI

IR = V - e^[R/L(c-t)]

IR = V - e^[R/L*(-t)] * e^(Rc/L)

I = V/R - e^[R/L*(-t)] * e^(Rc/L)/R

assume A=e^(Rc/L)/I since no parameters are given and i don’t have psykinetic powers

I = V/R - Ae^[R/L*(-t)]

(Source: phratria)