For a simple L-R circuit , I = I... (the exponential expression) . The text says that its defined for t >= 0 but when we talk about the voltage of the inductor,
it's defined for t >= 0+.
Moreover what difference does '+' make when t > '=' 0?
Please tell the reason for this.

 

If you have taken calculus you will appreciate the difference. If you haven't, then take it on faith, that in order for there to be any non-zero voltage across the inductor there must be a change in current even if the change is measured over an infinitesimally small time increment.

 

For a simple L-R circuit , I = I... (the exponential expression) . The text says that its defined for t >= 0 but when we talk about the voltage of the inductor,
it's defined for t >= 0+.
Moreover what difference does '+' make when t > '=' 0?
Please tell the reason for this.

While the current through an inductor MUST be continuous (since energy is continuous and the energy stored in an inductor is a function of the current), the voltage across it does not. Usually in the situation you are describing something has changed in the circuit (the proverbial switch is open or closed at t=0). The voltage thus jumps instantaneously from what it was just before the switch was thrown to what it was just after the switch was thrown. The voltage across the inductor at the moment the switch is thrown is undefined.

 

For a simple L-R circuit , I = I... (the exponential expression) . The text says that its defined for t >= 0 but when we talk about the voltage of the inductor,
it's defined for t >= 0+.
Moreover what difference does '+' make when t > '=' 0?
Please tell the reason for this.

Hello there,

What text is that?

I ask because
v=L*di/dt

but when you apply a voltage to a resistor and inductor in series, the voltage appears across the inductor immediately, although we might say that it is at t>0 because of the unit step, but then again the unit step has two definitions where one defines the behavior at t=0 also and assumes it is non zero.

So anyway it is best to show the complete circuit and any associated information such as when any switches are thrown, in exact terms.