Math dilema

[Simon]

Attached is a portion of my maths studies, the first part of the 37.5% that makes up a HNC in electrical engineering, maths

I can't see how the first formula becomes the second, if i = 0 when t=0 and using this scenario demonstrates the second formula I struggle to see how iR is still there because if t=0 then 0xR=0

[apis]

I can't see how the first formula becomes the second, if i = 0 when t=0 and using this scenario demonstrates the second formula I struggle to see how iR is still there because if t=0 then 0xR=0

You only use i=0 and t=0 to determine C, then replace C in the first expression with what you found.

[Simon]

oh I see, thank you

[IanB]

Background to this. The first equation was obtained by integrating another equation that describes the rate of change of current in the circuit (integral calculus). When you integrate something you always get "plus a constant" in the answer. To find the constant you have to plug in some numbers that you know, for example the initial condition of the system (the state at time zero). In this example we know that at time zero (the instant when the switch is closed), the current must be zero (because there is some inductance in the circuit). So using the knowledge that t = 0 means i = 0 allows the unknown constant C to be determined.

[Simon]

unfortunately i am dumb when comes to maths and this is just the start of the course so i was hoping for it to be a bit more verbose.