00:01
So in this problem, we are given a circuit with several different resistors, some in series and some in parallel, and we are told to find different properties about this circuit.
00:11
So the main equation we're going to be using is, in addition to oms law, is the equivalent resistance over parallel resistors and series resistors.
00:22
So in parallel, the equivalent resistance is calculated by taking the sum of the inverse resistances and taking the inverse of the sum, and in series, it's just the sum of the resistances.
00:35
So for instance, the equivalent resistance from point a to point b in our circuit is the sum of the inverse of the three resistances in parallel, all taken an inverse.
00:48
So it would be one -half plus one -third, plus one -fourth, sum together and taken the inverse.
00:53
And plugging that into a calculator, we get 0 .92 oms.
00:58
Similarly, the resistance for between the point c and e is the inverse of those resistors summed and taken the inverse again.
01:08
And that would be one -half plus one -sixth, plus one -eighth, all taken an inverse.
01:13
Plugging it into a calculator, we get 1 .26 oms.
01:18
Now, once these resistances are found, the equivalent resistance of these two and resistant or four are in series.
01:27
So to find the total resistance of the entire circuit, we would sum the three resistances.
01:34
So we take 1 .62 plus 0 .92 plus 2 to get the total resistance of the entire circuit, which is equal to 4 .54 ohms.
01:45
Okay? to get the total current throughout the entire circuit, we simply use oms law now that we found the equivalent resistance of the entire circuit.
01:57
The voltage through the circuit is just 15 volts.
02:00
So we divide the voltage by the resistance, and we get 3 .3 amps.
02:10
To find the current through specific resistors, what we have to do is we have to recognize that in parallel, the voltage across all three resistors is going to be the same, but the current is going to be different...