00:01
For this problem, we're asked to find this current, this resistance, and then this voltage drop.
00:05
So to find i, i'm going to use kirchhoff's current law at this node right here.
00:11
This blue one right there.
00:14
And kirchhoff's current law says that the current in is equal to the current out.
00:20
So we have that i plus 1a, 1 amp, this is equal to 6 amps.
00:28
And then we can subtract 1 amp from both sides and we get that i, this is equal to 5 amps.
00:36
So this is the current.
00:39
And then now to find r, i'm going to use kirchhoff's voltage law around this first loop, which says that the sum of the voltages across that loop, they're all equal to 0.
00:51
So if i start here, then i hit the 18 volts first, and i hit the positive terminal.
00:57
So this is plus 18 volts.
01:01
And then i come across this resistor of 2 ohms, and then one current is going through it.
01:06
So the voltage drop is 2 volts, plus, i could also write this as 1 amp, and then times 2 ohms.
01:19
And then lastly, i have this final resistor r.
01:22
So i'm going in the opposite direction of i.
01:26
Therefore, i have to include that as a negative sign...