Question

In a circuit containing Inductance L, resistance R, Voltage E. The current I is given by E=RI+dI/dt. Given L=640H,R=250 ohm, E=500v. I being zero if t=0.Find the time that elapse before it reaches 90% of its maximum value?

Answer 1

Answer:

Solution:

The given equation didt+RiL=EL is linear of the type dydx+Py=Q

∴ Its solution is ie∫R/L dt=∫e∫R/L dt⋅EL⋅dt+c

i.eRt/L=EL∫eRt/Ldt+c=EL⋅eRt/LLR+c=EReRt/L+c

When t=0 and i=0∴c=−ER

∴ i. eRt/L=EReRt/L−ER

∴i=ER(eRt/L−1)

∴i=ER(1−e−Rt/L)

Step-by-step explanation:

The given equation didt+RiL=EL is linear of the type dydx+Py=Q

∴ Its solution is ie∫R/L dt=∫e∫R/L dt⋅EL⋅dt+c

i.eRt/L=EL∫eRt/Ldt+c=EL⋅eRt/LLR+c=EReRt/L+c

When t=0 and i=0∴c=−ER

∴ i. eRt/L=EReRt/L−ER

∴i=ER(eRt/L−1)

∴i=ER(1−e−Rt/L)