00:01
Welcome to this numerate tutorial.
00:04
So a practical note analysis method for the first problem figure 4 .3 .9 is the first draw out the circuit and identify the labels here.
00:20
And then we must trace the dc electron flow from both battery terminals, which flows from positive to negative.
00:30
So if we figure out which way the electron flow is going, we essentially have a combined series parallel dc complex circuit with two batteries.
00:49
And the top current flow specification is specifying 10 amps across the left and the right side on the two battery power sources.
01:05
So from that point on, we can combine the 3 -oom resistor with the 6 -oom resistor and the 30 -oom resistor because just on the left side, they can be combined into a series cumulative addition of resistors.
01:29
So we have 48 oms total resistance on the left side.
01:35
So starting from the 240 volt battery, the flow is from positive to negative.
01:45
And this first circuit pathway is completely series, which means the current will remain constant.
01:57
So we can take 240 and divide it into the left side total resistance to compute 5 amps, constant current flowing on the left side.
02:10
For both the left and the right side on the same series circuit, there's a total of 10 amps.
02:16
So we know whatever remains on the right side is going to be 5 amps.
02:23
So v1, for the voltage drop at resistor 3 oms, will be the 5 amp calculation times 3 oms.
02:37
This is oms law.
02:39
E voltage is equal to i ampers times.
02:45
Resistance so we have 15 volts for v1 and then if we go to the right side and we look at this battery kind of on a mirror image it's the same thing but it can get kind of confusing so if we were just ignore the left side and combine the 30 and the 12 om resistor we would then have a series addition for a cumulative or i'm sorry a total resistance on the right side of 42 oms.
03:29
So v2 would be equal to the remaining amp here's because if the 10 amps stopped here, we'd have to then compute the total resistance with relationship to the 60 volt battery.
03:45
But we do have a specification.
03:47
And obviously at this node, there's some sort of a diode that takes the electron flow from the right battery and flows it like this.
03:57
And then the left battery it flows it like this back so we have a balance that's established and so the v2 will equal the voltage drop at the 12 -oom resistor so we have 5 amps times 12 oms it becomes 60 volts dc for v2 so the power at the 6 ome resistor is equal to the current times the voltage i .e.
04:40
So if we take the current 5 amps, then multiply at times the voltage drop.
04:49
5 amps times 6 oms, that's 30 volts times 5 amps.
04:57
So the power dissipated at 6 ome resistor is 150 watts.
05:05
So this is figure 4 decimal 39.
05:17
As for figure 4 decimal 57, this problem is essentially an exercise in an imbalanced circuit with insufficient voltage to maintain the circuit specifications.
05:39
So if we draw this figure 4 decimal 57 out and isolate the specifications accordingly, the problem asked to solve for the i sub y value.
06:04
So we must first compute the total resistance of this dc series parallel complex circuit.
06:24
So if we start with the 4 -oom resistor, we add it to the 3 -oom resistor.
06:32
We get 7 oms, and we combine that with a parallel 2 -oom resistor, the first one on the right, using the product sum rule.
06:42
So we multiply the combined series 3 -oom resistor with a 4 -oom resistor 7, 7 times 2 divided into 7 plus 2.
06:55
And then that combines to 1 .56 oms, then plus 1 .6 oms, then plus 1 .6, since it's in series with the combined 1 .56 -oom resistor.
07:13
Resistor, this then becomes 2 .56 oms, then combined with the 2 ome resistor.
07:35
So 2 .56 oms times 2, divided into 2 .56 oms plus 2 oms, so 4 .56 oms.
07:47
And this then becomes 1 .13 oms, then simply combined with with the 5 -oom resistor.
08:02
And then we have 6 .13 oms total resistance.
08:11
So the e sub t, the total voltage is 10 volts.
08:18
We then divide that into the total resistance, 6 .13...