00:01
This question is an underground cable of 10 kilometer long extends east to west and consists of two parallel wires, each of which has a resistance of 15 oms per kilometer.
00:11
Electrical short develops at the distance of x from the west and when a conducting path of the resistance r connects the wires, the resistance of the wires in the short is 140 ome measured from the eastern and is from here and is 190 when measured from the western.
00:28
So what is the value of x and r? let's talk about east side first.
00:36
If we measure the resistance from the east side, which is from here, the circuit is going to look something like this, because there will be some resistance of the upper wire, some resistance of the short, which is r, and some resistance of the return wire.
00:52
So if this is x, we know that the total is 10, so that's going to be 10 minus x kilometer.
00:59
And the resistance is given by 15 om for one kilometer.
01:02
So definitely that's going to be 15 times 10 minus x for the, you know, the total length of 10 minus x and likewise 15 times 10 minus x for the return length as well.
01:12
So what is the total resistance? the total resistance is going to be 15 times 10 minus x plus r plus 15 times 10 minus x.
01:21
So if you open up the parentheses and in fact these are two identical terms.
01:25
So that's twice of this.
01:27
So basically i can write 30 times 10 minus x.
01:29
X because i mean i hope it makes sense because basically this is twice of this or twice of 15 times 10 minus x plus r twice of 15 is 30 so we have 30 times 10 minus 10 minus sorry twice of 15 times 10 minus x plus r so that's 30 times 10 minus x plus r which is nothing but 300 minus 30 x plus r and this is nothing but 140 as given in the question so um if you rearrange then i think subtracting 140 both the sides, then we'll get 160 because 300 minus 140 is 160...