I too have got my principles exam next month C&G 2365 202, been doing lots of revision and always stumble on star/delta formulas, just cannot remember which way round they are.
Alright, how's this:
The first thing to clock is what we mean by line and phase. I think of "line" as the connections (imagine a red 3-phase commando socket), so your line current would be current going to one of the pins on the socket, and your line voltage would be between two of the line connections (L1 to L2, or L2 to L3, or L3 to L1). I think of "phase" as the windings on the supply transformer - the squiggly symbol that looks like an inductor. So phase voltage would be voltage across one of these squiggles, and phase current would be the current through one of these squiggles.
You know that on one of them (star/delta) the current is the same (I[SUB]L[/SUB]=I[SUB]P[/SUB]), and on the other one the voltage is the same (V[SUB]L[/SUB]=V[SUB]P[/SUB]) but which way round? Also, maybe you know that, but can never remember whether it's V[SUB]L[/SUB]=√3 x V[SUB]P[/SUB] or vice-versa.
For the first one of these:
Star is the only one with a neutral. So the voltages must be different, as on delta you can only measure between any two lines and you'll always get the same voltage.
As for which is the bigger number, V[SUB]L[/SUB] (or I[SUB]L[/SUB]) or V[SUB]P[/SUB] (or I[SUB]P[/SUB]), consider this:
On a single phase system, you'd say "the voltage is 230V." This is between a line and neutral, in other words, across one of the squiggly bits on your picture, so it's the phase voltage (V[SUB]P[/SUB]).
On a three phase system, you'd say "the voltage is 400V." This is between two lines, so it's the line voltage (V[SUB]L[/SUB]).
So V[SUB]L[/SUB] must be bigger than V[SUB]P[/SUB]. So V[SUB]L[/SUB] = √3 x V[SUB]P[/SUB].
And on delta, what about the currents? The rule is: same relationship. So in both cases, line (voltage on star, current on delta) is bigger than phase (voltage on star, current on delta. So on delta, I[SUB]L[/SUB] = √3 x I[SUB]P[/SUB].
Hope that's helpful.
