00:02
Hello students, in the first question this is a given circuit in the question and there are five resistors given in the question with 2 ohm, 5 ohm, 4 ohm, 3 ohm and 1 ohm and the voltage supply is 12 volt and 20 volt across the circuit.
00:18
So first let's find out at node 1 that is v1 so v1 this is a node v1 and this is node v2.
00:33
So at node v1 the current i is equal to i1 plus i2 hence we can write it as 12 minus v1 by 2 which will be equal to v1 by 5 plus v1 minus v2 divided by 1 therefore we will get 6 is equal to v1 divided by 5 plus v1 by 2 plus v1 minus v2 divided by 1 hence on substituting the values we will get 2 v1 plus 5 v1 plus 10 v1 minus 10 v2 divided by 10 hence we will get the equation as 17 v1 minus 10 v2 will be equal to 60.
01:30
Let's mark it as equation number 1.
01:32
Now at the node v2 the equation will be i2 plus i4 equal to i3 it will be equal to v1 minus v2 by 1 plus 24 minus v2 divided by 3 will be equal to v2 by 4 therefore v1 minus v2 by 1 plus 8 minus v2 by 3 minus v2 by 4 will be equal to 0.
02:08
So on further simplification we will get 12 v1 minus 12 v2 minus 4 v2 minus 3 v2 divided by 12 which will be equal to minus 8 hence we will get the equation as 12 v1 minus 19 v2 which will be equal to minus 96 and mark it this equation as equation number 2.
02:37
Now on solving equation 1 and equation 2 we will get v1 as 10 .344 volt and v2 as 11 .586 volt.
02:53
So now let's find out the input current that is equal to v2 minus v1 divided by 1 for that we'll get the answer as 1 .242 ampere so the required answer here is the input current is equal to 1 .42 ampere.
03:18
The next question is the figure for the question is this so we need to find out the current through the 20 ohm resistor we need to find out the i20 here so let's calculate it by solving it for each nodes one by one at v1 we can write v1 minus 20 divided by 5 plus v1 plus 10 plus v1 minus v2 by 10 will be equal to 0 therefore on taking the lcm we'll get 2 v1 minus 40 plus v1 plus v1 minus v2 divided by 10 will be equal to 0.
04:07
So we'll get the v1 minus v2 will be equal to 40 and mark it as equation number 1...