00:01
All right, for this problem, let's draw the circuit diagram first.
00:06
First of all, we have a source here.
00:09
With this source, we have a resistor connected.
00:11
With this register, we have another register connected.
00:15
And with this resistor, we have one more resistor connected, and this is connected with the negative terminal of the battery.
00:22
And from this node, we have one another register connected, and with this register, another register is connected like this way.
00:30
And this resistor is connected to this node now let's label the circuit components this potential or the voltage source it is of 20 .6 volts this resistor it has been labeled as r1 and it is of 3 oom this resistor it has been labeled as r2 and it is again of 3 oom this resistor it has been labeled as r3 again of same rating this resistor are four again of same rating three ohm and finally this resistor it is r5 and it is again of three ohm all right now in the first part of the question we have to find the total resistance or the equivalent resistance of this whole circuit now let's analyze the circuit in this circuit this resistor and this resistor they are in series it means if they are in series they should be aired r1 plus r2 as a result of these two resistors we will get one resistor and that resistor will be in parallel with r3 it means it will be parallel with rolite so the collection of these three registers will give us one resistor here and this one resistor will be in series with r1 all right r1 and there the both the combination of this resistor and this resistor it will again be in series with r4 all right so this is the expression now let's plug in the values r1 it is of 3 ohm r2 it is again of 3 ohm it means it is 6 ohm is in parallel with r3 it is of 3 ohm all right this r1 it is of 3 ohm and this r4 it is again of 3 ohm all right 6 in parallel with 3 ohm this would simply be equal to 6 multiplied by 3 divided by 6 plus 3 so this is the parallel combination plus 3 plus 3 is 6 ohm all right from here 6 plus 3 is 18 18 divided by 6 plus 3 is 9 18 divided by 9 is 2, 2 plus 6 is 8.
03:12
It means r equivalent or the total resistance of this circuit comes out to be 8 oms.
03:20
So this is part a.
03:23
For part b we have to find the current flowing in this resistance, this r2.
03:28
Let's label this current i and let's say this is our node a and the potential of this node is let's say we a.
03:38
To solve this current we will use this method this method is called nva or nodal voltage analysis at which node at node a according to this analysis or according to this formula the sum of all the currents at this node should be equal to zero so there are three branches connected with this node it means there should be three currents one one current from this branch the other current from this branch and the last current will be flowing from this branch.
04:12
For that, let's say this node is at the ground.
04:17
All right.
04:17
Means it is at zero volts.
04:21
First of all, this current.
04:25
We will calculate this current...