00:01
Hi, in this question for this circuit shown we have to calculate the current for the 6 volt voltage source using node voltage analysis.
00:11
So here if we let that unknown branch currents are i1 so here the current i1 is flowing in this particular branch we have i2 in this particular branch we have i3 here we have current i4 so here the current i6v is already mentioned.
00:34
So if we apply node voltage method or nodal analysis to find voltages and branch currents so first of all we will see at node 1 so at node 1 we can write i1 plus i2 plus i3 will be equals 0.
00:55
So we will have v1 minus v2 divided by 6 plus v1 minus v0 divided by 8 plus v1 minus v3 by 12 equals to 0.
01:08
So on solving this equation we get 0 .375 times v1 minus 0 .167 times v2 minus 0 .083 times v3 equals to 0.
01:22
So this is equation 1.
01:24
Now we apply the same at node 2 so at node 2 we can write minus 0 .5 plus i4 minus i1 equals to 0.
01:38
So this will be minus 0 .5 plus v2 minus v3 divided by 8 plus v2 minus v1 divided by 6 equals to 0.
01:49
So now on solving this further we get the expression as minus 0 .167 times v1 plus 0 .292 times v2 minus 0 .125 times v3 equals to 0 .5.
02:09
So this is equation number 2...