Assignment:
An electric circuit with an ohmic resistor R and an inductance L will exhibit a certain delay in approaching the (asymptotic) saturation current I_infinity=U/R in response to a voltage source U. Using Kirchoff's circuit laws, electrical engineers have proposed the equation
dI/dt=-R/L I+U/L for describing the time dependence I(t) of the electric current.
If the electric current is zero at time t=0, determine the solution I(t) in terms of the given constants U,R, and L.
Electrical engineers are often interested in the time T when the electric current I reaches 75% of its saturation value. Determine the value of T in terms of the given constants.
Assuming a circuit with U=200V,R=50 ohms,L=100H, when is the electric current 0.5A below the saturation level? You may ignore the units here (they are all SI).