00:01
Okay, so since we need to know the current through each resistor in this figure, we can see that each resistance has a value of 3 .25 kilooms and the voltage of the battery is 12 volts now to get the current we first need to find the total current that's passing through the circuit because if we look at this resistor so this is in series connection with this guy so that means and since this is directly connected to the battery that means the whole current is passing through r6 so that means we need to know the full current and to do so we can actually simplify the circuit and as you can see i have simplified the circuit till this end and let me explain what i did here so first of all as you can see between a and b r1 and r2 is in series connection so i replaced r1 and r2 by r12 and then the rest of the circuit is the same but then between point a and b r1 2 and r3 are in parallel connection so i replace them with this and r1 2 3 so this is the circuit new circuit and then as we can see that between points a and c r1, 2, 3 and r4 is in series connection.
01:35
So we replaced these two guys by this equivalent circuit, which is r1, 2, 3, 4.
01:42
And then we have parallel connection of r1, 2, 3, 4 with r5, and we replace that by r1, 2, 3, 4.
01:51
And then this resistor is in series connection with r6, so we replace them by rq.
01:57
Now we can actually find out all the values for these registers so let's get on to it so first we need to find r1 2 so that's gonna be r1 2 which is equal to r1 plus r2 and since they're all they all have the same resistance so that's going to be r plus r which is two times r then for r one two three this is going to be since it's a parallel connection between r one two and r three it's going to be this and then we'll have one over r one two plus one over r three reciprocal and if we plug in the expression for those we get 2 over 3 r so you guys should try doing it by yourself so that you get some practice okay moving on so now we have a series connection so that means r 1 2 3 4 is going to be 2 3 4 is going to be r 1 2 3 plus r 4 and which is nothing but 5 over 3 r then then we have a parallel connection so r one two three four five that's going to be one over r one two three four plus one over r five reciprocal and that gives us five over eight r right and finally our equivalent equivalent that's going to be a series connection between r, 1, 2, 3, 4, 5, and r6.
04:08
And that's going to be, let me write that down.
04:11
1, 2, 3, 4, 5, 6 plus r.
04:16
Sorry, it's going to be 1, 2, 3, 4, 5, and r6.
04:24
And that is going to be 13 over 8 r.
04:30
Right.
04:31
So now we know how we simplified the loop.
04:35
Now we can go backwards and because we need to go backwards to get the current because so that's our equivalent resistance and we know the total voltage so using ohm slow we can get the equivalent current so that's going to be ieq which is equal to the voltage of the battery over the equivalent resistance and if we plug in the values here um or uh let's just plug in this guy over here and we get 8 epsilon over 13r and this guy right here is same for r6 and r1 2 345 because as we saw that this is a series connection so the current passing through this circuit and this circuit will be the same so this guy is equal to r i6 which is equal to i 1 2 3 4 5 right and then if i look at the circuit diagram again we see that v5 so v5 is the voltage difference between a and c and so this guy is equal to v 1 2 3 4 because it's a series connection and that's equal to v 1 2 3 4 because again this whole guy is this circuit so let me write that down so it's going to be v5 which is equal to v v 1 2 3 4 which is v 1 2 3 4 5 and according to our own slow it's going to be 1 2 3 4 5 times r 1 2 3 4 5 and if we replace the values we'll get 8 epsilon 13 or r multiplied by 5 over 8 r so this guy right here is r 1 2 3 4 5 which is this right and i 5 so i 5 is going to be v5 over r5 and that's going to be v5 over r5 and that's going to be 5 by 13 epsilon over r, which is 5 epsilon over 13r.
07:37
And yeah, that's our i5...