Resistive AC circuit - Alternating Current Video Lecture - Class 12

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currents part 3 is brought to you by
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make sure that you have watched all the
videos still part 2 before going ahead
with this part I'll start with resistive
AC circuit that needs and a society
which will have only resistors it will
not have any other circuit elements so
we will talk about what happens when an
AC voltage is applied to a resistor now
before that let me tell you as an piece
of DC power supply view normally
represented this way so when it comes to
AC power supply it would be represented
with this symbol so this is the symbol
for it
AC power supply so this is your AC power
supply and in the circuit you have
nothing else but a resistor with
resistance I right so we will see that
what happens when we give AC voltage
need this the resistor that means we
want to see how much current will flow
through the circuit what would be the
voltage I mean what would be the
alternating current here what would be
the alternating voltage here and what
would be the relation between voltage
and current and the what what should be
the power consumption of this circuit so
we will talk about all those things one
by one let us start with very basics so
if I say that this is my alternating
voltage source so let us say that my
input AC voltage is V and that V is
nothing but VM sine Omega T right where
what is VM VM is nothing but the peak
value of voltage right you remember in
the first slide I told you the voltage
will vary somewhat like this so the pink
value which voltage will reach that is
VM so this is often known as voltage
amplitude it is also called as voltage
amplitude like
you are aware of the term amplitude
right when we talked about oscillations
we said that amplitude is nothing but
the maximum displacement from the mean
position so here also if you see it is
nothing but the maximum displacement
from its mean position mean position is
nothing but the origin so the maximum
how much it is going it is going to its
peak right so this VN is known as peak
value and alternatively it is also known
as voltage amplitude so now we will
apply Kirchhoff's loop rod loop rule to
this circuit so according to Kirchhoff's
loop rule what do we know we know that
the total EMF of this circuit should be
equal to the sum of the product of the
current and the respective resistances
in the circuit like this is microsoft's
loop rule so if you have forgotten your
cha-cha nodes please get back to the
previous lessons and go through them
because one important thing is that
whenever you study a particular chapter
make sure that you are studying in
sequential that means because see in
this chapter I talk about resistors
capacitors inductors and talk about the
chops rules so it is good if you have
gone through those lessons in that case
you will not find difficulty in
understanding these concepts because I
will not talk about everything in detail
because pitch options are something
which I have already spoken in my
previous lesson right okay so what does
get chops unit it says that the total
EMF in the circuit will be equal to the
sum of the product of current and
resistances in the entire circuit so now
let us suppose that the EMF of this
voltage sources e for now let me call it
as E or let me keep it as V to avoid
further confusion as I told here that
input voltage is V so let me call it as
B so according to kirchoff's law what
would be the total EMF of the circuit it
is nothing but V because it is the only
source of EMF here so this way should be
equal to the sum of all the resistances
the sum of product of current
and resistances in the entire circuit so
there is only one resistance in this
circuit so this will be equal to I into
I if I assume that current flowing
through the circuit is i if I assume
that the current flowing through the
circuit is I now what is this V V is
nothing but VM sine Omega T so this is
equal to I so we can say that I is equal
to VM divided by R sine Omega T so that
means this is the amount of current
which will flow through them set it now
we replace this term VM by ad with I M
where I am is nothing but analogous to
voltage this I am would be the current
amplitude for the peak value of current
right so in this case this I M is your
current amplitude or the maximum value
of current so even so what do we get to
go to the see from here we see that if
we apply an alternating voltage to a
circuit where we have just a resistor in
that case the current flowing through
the circuit will also be an alternating
current that means the current flowing
through the circuit will also be a
sinusoidal function right so we see that
here the current flowing through the
circuit will be I am sine Omega T where
I am is the current amplitude or also
known as the peak value of current so we
will try to graphically represent the
relation between the voltage and the
current in case of a resistive circuit
so let us do that if this is the graph
your voltage is assigned sinusoidal
function so this blue line represents
the variation of voltage and the green
line represents the variation of current
C both are sine functions but if you see
that the value of the peak value of
current or the current amplitude is
lesser than the voltage
amplitude why is it so because from the
previous slide you can see that connect
amplitude is equal to voltage amplitude
divided by R right from our previous
slides we saw that current amplitude is
equal to voltage amplitude divided by a
so that means current this shows that
current amplitude is lesser than the
voltage amplitude so that is why the
maximum or the peak value of current
would be lesser than the peak value of
voltage right but at the same time we
also see that both of them are in the
same phase so that is why both of them
reach their maximum value at the same
time they reach zero at the same time
they reach their minimum value at the
same time that means they both had n
things I have already spoken about phase
phase differences topics in my previous
lessons of class 11 so please go through
them in case your concepts are not clear
about phase so then when we talk about
phase we can have a look at these
expressions that is V is equal to VM
sine Omega T and correct which this V
produces is I M sine Omega T so by
looking at these we can say that V and I
will reach their minimum maximum 0 at
the same time because when T is 0 sine 0
will be 0 so V will be 0 I will also be
0 so basically they are in the same
phase that means they reach their
maximum they reach their minimum they
reach 0 at the same time so what is the
this is how we can represent it
graphically that the relation between
voltage and current as that they are in
phase with each other right and the peak
value of current is lesser than the peak
value of voltage now when we talk about
the average current now till now we
spoke only about peak value of current
and peak value of voltage the other
value which we can talk about as that is
Dainius value of current or voltage
because an alternating current the value
is changing at every instant of time so
the value will be if you look at the
voltage curve the value of voltage at
every instant that is known as the
instantaneous value of voltage so this V
is nothing but it represents the
instantaneous value of voltage at time T
similarly this I represents the
instantaneous value of current at any
time given by this T what would be the
average current over a complete cycle
what is the cycle a cycle is nothing but
starting from zero and reaching 2pi and
then again the same pattern for those
right so one cycle would mean zero to
2pi so that in average current over this
complete cycle is zero that's because
this positive this negative will cancel
out so the average current is zero
similarly the average voltage over a
complete cycle is zero right so I hope
now you understood that what is the
relationship between an alternating
voltage what happens when we give or
when we apply an AC voltage to a
resistor we get an alternating current
which is in phase with the applied
voltage right the average current over
one cycle is zero the average voltage
over one cycle is zero thank you please
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