# If the rule of thumb is "wait 3tau" wouldn't this mean the magnet is taking longer to discharge if the time we need to wait is 4.61tau

#### Mojo Pin__

Joined Apr 13, 2019
83
In this lecture we are looking at an example of a superconducting magnet which needs a resister to discharge from it's maximum field in 1 minute. Everything made sense until the last line of the image I have attached. We have been told that by rule of thumb you should wait 3tau (3 times the time constant) for the discharge to reach an adequate value. So when the professor says 4.61tau is shorter than the rule of thumb (3tau) and "the rule is on the safe side" I am confused, can someone help me understand this please?

#### Delta Prime

Joined Nov 15, 2019
1,311
To confuse you was intentional. Don't play it safe no one does

Last edited:

#### WBahn

Joined Mar 31, 2012
27,406
In this lecture we are looking at an example of a superconducting magnet which needs a resister to discharge from it's maximum field in 1 minute. Everything made sense until the last line of the image I have attached. We have been told that by rule of thumb you should wait 3tau (3 times the time constant) for the discharge to reach an adequate value. So when the professor says 4.61tau is shorter than the rule of thumb (3tau) and "the rule is on the safe side" I am confused, can someone help me understand this please?
Let's rephrase things to make it a bit clearer.

We are interested in the current at a particular time, T.

The smaller the time constant, the lower the current will be at time T, right?

That time will be some multiple, N, of the time constant, T = N·τ

So the time constant is τ = T/N

The bigger N is, the smaller the time constant will be.

#### Mojo Pin__

Joined Apr 13, 2019
83
Let's rephrase things to make it a bit clearer.

We are interested in the current at a particular time, T.

The smaller the time constant, the lower the current will be at time T, right?

That time will be some multiple, N, of the time constant, T = N·τ

So the time constant is τ = T/N

The bigger N is, the smaller the time constant will be.
Thank you for your advice, rephrasing it helped me understand the whole thing a bit more.

When I'm going through his notes I think he meant to say that for this particular example 5tau was recommended but it turns out 4.61tau is what we calculate so 5tau was "playing it safe".

You said "the smaller the time constant the lower the current will be."

But wouldn't the current be at its highest at the very start of the transient when tau is at its lowest?

#### WBahn

Joined Mar 31, 2012
27,406
Thank you for your advice, rephrasing it helped me understand the whole thing a bit more.

When I'm going through his notes I think he meant to say that for this particular example 5tau was recommended but it turns out 4.61tau is what we calculate so 5tau was "playing it safe".
If you decide that 5τ is what will be deemed "playing it safe", then if the time of interest is only 4.61τ you will not have waited 5τ at that time, you will only have waited 4.61τ. But if you decide that 3τ is sufficient to be considered "playing it safe", then waiting 4.61τ will be waiting longer than 3τ and so will be even safer, right?

You said "the smaller the time constant the lower the current will be."

But wouldn't the current be at its highest at the very start of the transient when tau is at its lowest?
Yes, the current is at it's highest at the very start of the transient and that current is completely independent of the time constant. The time constant (which does not change -- there's a reason they call it the time "constant") governs how quickly the transient dies off AFTER the start of the transient.

#### Mojo Pin__

Joined Apr 13, 2019
83
If you decide that 5τ is what will be deemed "playing it safe", then if the time of interest is only 4.61τ you will not have waited 5τ at that time, you will only have waited 4.61τ. But if you decide that 3τ is sufficient to be considered "playing it safe", then waiting 4.61τ will be waiting longer than 3τ and so will be even safer, right?

Yes, the current is at it's highest at the very start of the transient and that current is completely independent of the time constant. The time constant (which does not change -- there's a reason they call it the time "constant") governs how quickly the transient dies off AFTER the start of the transient.
thank you! yeah I hadn't realised the difference between the time and the time constant, tau is constant but the time changes, seems pretty obvious once that clicked, I think I get it now.

#### MrChips

Joined Oct 2, 2009
27,129
In post #1 the text states:
Remember that a larger value of R gives a smaller value of τ.
Either this is typo or I am missing something.

In a resistor + capacitor charge/discharge circuit,
time constant is
τ = RC

#### OBW0549

Joined Mar 2, 2015
3,566
Either this is typo or I am missing something.
In a resistor + capacitor charge/discharge circuit,
time constant is
τ = RC
He's talking about a resistor-inductor circuit, not a resistor-capacitor circuit.
So τ = L/R, and a larger value of R does indeed yield a smaller value of τ.

#### WBahn

Joined Mar 31, 2012
27,406