# Voltage Lead in an AC inductive circuit?

#### Weasel

Joined Mar 25, 2006
3
Hi folks,

This site has been very useful to support my studying for a desperately needed exam pass. My own training notes use this mnemonic to help remember lead/lag details: CIVIL. You probably have seen it but just in case not : in a Capacitive circuit, I (current) leads V which (itself) leads I in an inductive (L) circuit.

My problem is that I'm absolutely dreading the exam and would rather like to understand the thoery (as a backup) rather than just remember CIVIL.

I have read Vol2 CH3 AC Inductor circuits on this site, which has been a Godsend but it tells me (quote) 'Remember, the voltage dropped across an inductor is a reaction against the change in current through it'.

Surely this describes that the current must change BEFORE the voltage drops as a reaction, and that I leads V in an L circuit ?

This is probably all common knowledge to you guys but having been a nuts & bolts man for 30 years, the electric string stuff is not an easy conversion for me. I just cannot get any deeper into 3 phase AC generation till I understand this bit. If anyone can provide an explanation, it would help a lot, thanks.

#### n9xv

Joined Jan 18, 2005
329
Think of it this way,

for capacitors;

I leads V because the current must flow to the plates of the capacitor before it can be charged up to the applied voltage.

for inductors;

When current first flows through the inductor it generates a voltage across the coil. This generated voltage has a polarity such that it will try to oppose the current thats generating the voltage across the coil. This opposition to current means that the "generated" voltage appears first and then "opposes" the current flow thus causing the current to lag the voltage.

#### Weasel

Joined Mar 25, 2006
3
Originally posted by n9xv@Mar 25 2006, 08:33 PM
Think of it this way,

for capacitors;

I leads V because the current must flow to the plates of the capacitor before it can be charged up to the applied voltage.

for inductors;

When current first flows through the inductor it generates a voltage across the coil. This generated voltage has a polarity such that it will try to oppose the current thats generating the voltage across the coil. This opposition to current means that the "generated" voltage appears first and then "opposes" the current flow thus causing the current to lag the voltage.
[post=15451]Quoted post[/post]​
Thanks for that n9XV. I think I'm OK with a capacitor as imagine, like a battery, it needs to eat a lot of current into it BEFORE it will show a volatage rise, but for the inductor even your explanation starts with the flow of current that then generates the back emf. It's still a bit chicken and egg I'm afraid. The only thing that I may have misunderstood might relate to what you say regarding 'appearance' of voltage and therefore perhaps that the initial current may not be apparent...Or am I just making things worse?

#### n9xv

Joined Jan 18, 2005
329
Well, try to walk through it on the "electron level". Electrons begin flowing in one end of the coil. As they flow, they generate a voltage across the coil. This generated voltage in turn opposes the inrush of current that produced it. I know that sounds redundant but maybe it would help to look at the circuit from the point at which the "generated" voltage appears across the coil. Then you can conceptualize the voltage opposing the continual flow of current.

In reality, current obviously had to flow first in order to produce the generated voltage that in turn opposses the initial flow of current. This initial flow of current "does'nt count" in terms of analizing the "phase angle" or lead / lag relationship.

With inductors - the egg initially came first, that egg turned into a chicken. Now we are only interested in the chicken that continually produces more eggs.

Did that put you deeper in the hole or pull you out?

#### Papabravo

Joined Feb 24, 2006
16,106
This seems like an opportune time to expound on the "Theory of Holes". In short
"When you find yourself in a hole -- stop digging". ROFL

I don't know if a mechanical analogy would be helpful, but try the following:
A spring exerts a force proportioanl to a displacement, x.
A shock absorber, dashpot, or damper exerts a force proprtional to a velocity, dx/dt

Think of a resistor as the electrical equivalent of a mechanical spring. A resistor creates a voltage proportioanal to a current, i.

Think of an inductor as the electrical equivalent of mechanical shock absorber. An inductor creates a voltage proportional to "current velocity", di/dt.

If I've dug the hole deeper, you have my sincere apologies.

#### Weasel

Joined Mar 25, 2006
3

From your explanation n9xv, I now think I'm clear it's the V that leads the I that causes the e, in that order.

I think PB you've spotted Ive perhaps been looking too deep.

My misunderstanding was/is that an instantaneous pos going di/dt (at max rate of change as it crosses the 0V line on the sine wave) would, in keeping with Lenzs Law, produce max neg emf. This would put the V at 90 degrees lag with ref to I. This seems feasible to me but isnt what the books state.

I read about the time constants under the heading of inductors in DC circuits, and that on closing the switch, the VL spikes, then dies away exponentially, whilst the current grows exponentially. This describes a lag.

Its a bit off-putting to find time constant info only under DC theory without even a mention under AC. Perhaps you could confirm I've got it right i.e that the 5T lag described under time constant theory is the SAME cause of the 90 degree I lag behind V on the AC sinewave graph, as the current struggles but never catches up with the ever-changing V.

Far simpler than the reasons I was dreaming up!

I'll probably be back again as the rest of the book doesn't look any easier.

#### Papabravo

Joined Feb 24, 2006
16,106
From our study of the calculus we know that if the current and voltage waveforms are sinusoids, then the maximum value of di/dt which is also a sinusoid at the same frequency, is limited. I think it is also possible to separate transient behavior from steady state behavior. In most AC analysis the assumption is that we are looking at the steady state. I don't remember spending much time thinking about sinusoids that are zero from t = minus infinity up to t = 0, and thereafter are sinusoids. Isuppose the other way to look at things is to bring the amplitude up slowly, but this has the same conceptual problems.