hello and welcome to my channel in today's video we will talk about RL
circuit and RC circuit and their time constants from where these time
constants come from and what is the significance of these time constants so
this we will discuss in this video and in the next video we will derive the
equation of currents for these two circuits so let's get started so the
first circuit is this circuit which is called RL circuit because we have a
resistor and an inductor so the value is to offer resistor and Henry's for
inductor and we have with like ten volts so when we close this switch initially
there is no current because inductor stores the uses the current to store the
energy but slowly this current starts to build up and then it reaches a maximum
value so for this kind of circuit the maximum value of the current which can
ever pass through this circuit is the current which is n divided by 2 this
resistor so this is five amperes so this is the maximum value of current which
this circuit can never pass on the capacitor circuit RC circuit it happens
in the opposite way so when we close the switch initially all the current passes
through the capacitor just like a short circuit then this capacitor starts to
charge and the current starts to drop and it reaches a value which is very
close to zero so this is what happens here and now these are the graphs and
these are the equations using these equations you can find the value of
current at any time so on this graph time is on the x axis and current is on
the y axis and this is the maximum value for capacitor circuit and this is the
maximum value of the inductor circuit so this is the brief introduction of what
is on this whiteboard at the moment and now let's talk about the time constant
so time constant of a decaying parameter any parameter it could be
it could be voltage currently we are using current so time constant for a
decreasing parameter is the time at which the time taken by the parameter to
reach 37 percent of its maximum value so we are looking for a six to three
percent drop so if this is the maximum value you can say 100% so this is the 63
percent draw of this value so that is the time taken for this is called time
constant so if you measure this time in seconds so that will be time constant
similarly for a rising graph the time constant is the time taken to achieve
the 63 percent of its maximum value so this is 0.63 so point 6 3 of the maximum
value so what is what is the time taken so if you drop a perpendicular and you
measure this time in seconds let us say
so this is one way of measuring the time constant if you have this graph so you
can just actually physically take this on a scale and then 63 percent of that
scaled draw perpendicular on this graph then draw perpendicular on x-axis and
calculate the time on here so this is the simple way of using the graph to
find the time constant but what is this time constant and we know when you not
only use the questions of these type of questions you use a time constant of / R
this is for other type of circuits these type of circuits we use time constants
and this is denoted by normally tau and for this type of circuits we use time
constants which is equal to RC or is the resistors is the capacitor value
capacitance value so these are the formulas so how we how we reach on these
formulas why we use these formulas for time constant so this is
what we are talking about in this video so no one step back
what is this point three seven point three seven is actually 1 divided by e +
1 divided by e is the base of the nature logarithm so 1 divided by E which is two
point seven eight something if you divide it you will get this point three
seven value so this is 1 divided by E and similarly this point six three is
basically 1 minus 1 divided by e in other ways you can say 1 minus point 3 7
h is 63 percent at 0.63 so basically there is only one factor which is 1
divided by E because if it's rising we just subtract it from 1 if it's this
decreasing we take this as it is so oh we got this as a value of L divided by R
because this is very important if we know I divided by R so we have Ln R
mentioned here so we can straight away tell the time constant of this circuit
and this gives us a very important information which I will describe later
but first from where we get these values so in order to understand this we have
to have a look at these equations which we will be driving and we will actually
see how we reach here but in this video I just want to explain how we get this
what this circuit will reach at this value and why how we can get these
values from these equations so now first we look at this equation so if you look
at this equation this is the value of the maximum and this is the factor which
we are looking for so this is the rising factor we want this vector this vector
equal to this T 1 minus 1 divided by e so if you look here and if you look here
this is e raised to the power minus R divided by L into T so now imagine what
value of T if I put here I get a raise to the power minus 1 only obviously the
value of T should be the reciprocal of this R divided by L which is L divided
by R if I put this value for T for time in this equation we will get 1 minus e
raised to the power minus 1 which is this factor because I raise to the power
of minus 1 means 1 divided by E so therefore this is the time constant of a
RL circuit because if I put this for time I will get I maximum x 0.63 this
value will make this part this factor 0.63 so therefore this is the time
constant of any RL circuit similarly for RC circuit what were you
of T if I put here which will make this thing as 1 divided by e so the value of
T should be RC if I put RC 40 here these two RC will be cancelled out and either
H to the power minus 1 will there which is 1 divided by E so therefore RC is the
time constant of a RC type of circuit in which we have a resistor and a capacitor
so these are the time constants no the the next thing is in most of the crops
you will see that instead of time you will miss you will see 1 tau 2 tau 3 tau
4 tau and five dow down Styne constant so sometimes these graphs instead of
time they denote this thing and why so because generally it is accepted that
after 5 time constants once the 5 time constants have been
elapsed the system will reach its final value or the steady state value which
will stay there so after 5
time constants the capacitor circuit will reach its minimum current and after
5 time constants the inductor circuit will also reach its maximum value 1 2 3
4 5 time constants so whatever is the value of the time constant let's take
this example the time constant of this circuit is L divided by R which is 10
divided by 2 which is 5 seconds so it means that after 25 seconds this circuit
will reach its maximum current value this is very significant because just by
looking at this circuit you can straightaway tell that when this circuit
will reach its maximum current by looking at this diagram only if you know
that the time constant is of this circuit is always RC so by looking at
our NC value you can straight away tell that let's say 15 to what 2 multiplied
by 3 is 6 6 second is the time constant so 5 time constants means 30 seconds so
after 30 second this circuit will be chased value so this is the importance
of time constant once you know how how we reach this so in this video I only
explained the end and the result the end of the equation from this equation you
can see that we can get the time constant values these values we not only
use these values without thinking from where these values are coming from so
this is the explanation of this time constant and in the next video we will
actually derive these two equations so really see that how we reach there so
thanks for watching and see you in the next video
you