Using the formulas for series and parallel circuits, fill in...

Key Concepts

Ohm's Law

Ohm's Law, which states that V = IR (voltage equals current times resistance), is the fundamental principle underlying circuit analysis. It is used to relate the voltage, current, and resistance in both simple and complex circuits, forming the basis for calculating unknown quantities when analyzing series and parallel components and their interactions.

Voltage Division Rule

The voltage division rule is used in series circuits to determine the voltage drop across a particular resistor by relating it to the total voltage and the ratio of that resistor's value to the total resistance. It provides a straightforward method for calculating how an input voltage is distributed among series-connected resistors, which is essential for understanding potential differences across components.

Current Division Rule

The current division rule is used in parallel circuits to determine the current flowing through an individual branch based on the branch's resistance and the total current entering the parallel network. It is derived from the relationship between current, voltage, and resistance (Ohm's law) and helps in analyzing how the total current splits across branches with different resistances.

Parallel Circuits

A parallel circuit is one in which the components are connected across the same two nodes, providing multiple paths for current flow. In a parallel configuration, the voltage across each branch is identical, but the total current is divided among the branches inversely proportional to their resistances. The overall resistance of a parallel circuit is found using the reciprocal formula, where the reciprocal of the total resistance equals the sum of the reciprocals of individual resistances.

Series Circuits

A series circuit is one in which components are connected end-to-end so that there is only one path for current flow. This means that the same current flows through all components, while the total voltage across the circuit is divided among the components based on their resistances. Analyzing a series circuit involves adding individual resistances to find the total resistance and applying the voltage division rule to find individual voltage drops.

Equivalent Resistance

Equivalent resistance is a concept used to simplify complex circuits by reducing a combination of resistors (whether in series, parallel, or a mix of both) to a single resistance value. In series circuits, resistances add directly, while in parallel circuits, the total resistance is obtained from the reciprocal of the sum of reciprocals of individual resistances. This simplification is crucial for analyzing overall circuit behavior, such as calculating total current or voltage.

Transcript

00:02 Here we've got a somewhat complex circuit with combinations of parallel sections and series sections or parallel sections a parallel section in series with individual resistors and primarily we're going to rely on just a couple rules and om's law.

00:27 Om's law being v equals irr and those rules being the rule for elements in parallel with each other, the voltage for two elements in parallel are going to have the same voltage drop as each other.

00:49 So the voltage of elements in parallel with each other have the same voltage.

00:54 And the rule for elements in series, the current rule in series, is that elements in series have the same.

01:05 Same current.

01:07 I guess we'll use one more rule to go along with that, and that is the junction rule, which is to say that the current into a junction has to equal the current out of a junction.

01:25 And i'll explain each of these as we go through this.

01:29 Some of these become, let's just label all the things we know to begin with.

01:36 So the battery's voltage is 35 volts.

01:41 The voltage drop at resistor 1 is 5 volts.

01:46 The current is 2 .75 amps.

01:50 2 .75 amps.

01:56 That's going to start to get pretty messy as we write stuff in, but we're going to be keeping track in our grid as well.

02:03 Resistor 2 has a current of 1 .95 amps.

02:12 Resistor 3 is 2 .8 oms.

02:19 At resistor 4, we know that it has a current of 0 .97 amps, and resistor 5 has a voltage drop of 7 .5 volts.

02:30 And we have no given information for number 6.

02:33 All right, let's start around the region of what's going on here in 1 and 2.

02:40 All right, voltage rule.

02:42 The voltage across parallel elements is the same for each one.

02:46 So that tells me that the voltage drop of number 2 is going to be 2 .75.

02:53 It's going to be 5 volts.

02:58 5 volts.

03:00 So at r2, it's going to have a 5 volt drop.

03:04 All right.

03:05 Now, if you know two pieces of information about an element, you can always find the third.

03:10 So let's find the resistance of each of those.

03:14 So the resistance, we rearrange the oum's law.

03:19 We got resistance equals voltage over current.

03:23 So if we do voltage over current for each of those, we get for number one, we get five divided by 2 .75.

03:30 That's going to give us a resistance of 1 .1 .82 oms.

03:42 And for resistor number two, we repeat that.

03:45 We got 5 divided by 1 .95.

03:52 We get a resistor of 2 .56 oms.

03:57 2 .56 oms.

04:01 Now, looking at number 3.

04:06 Kind of going clockwise along the way, we just determined that the current through number one and number two was 2 .75 and 1 .95.

04:21 The current, because current is actual electrons, think of it like water, you got two pipes flowing and those two pipes have to merge.

04:32 So the flow from one literally adds to the flow through the other.

04:37 And so the current through resistor number three has got to be the sum of those two together.

04:46 2 .75 plus 1 .95.

04:51 So the current through resistor number three is going to be 4 .7 amps.

04:58 4 .7 amps.

05:04 So now.

05:06 Now, as we said, if we know two things, then we can find the third.

05:10 So v equals i .r, but yeah, so i times r equals v.

05:20 So we've got 4 .7 amps times 2 .8 oms.

05:28 Gives us a voltage drop of 13 .16 volts.

05:37 13 .16 volts.

05:39 Alright, now i'm going to jump around a little bit, jump ahead a little bit, because as we said, using the series rule for things that are in series with each other, the current has to be the same.

05:55 So if the current through resistor 3 is 4 .7 amps, then sure, it's going to split two ways, but then it's going to rejoin from two ways, and that's got to be the same as the current through number six.

06:10 Where else is it going to go? it doesn't have any other choices.

06:14 So the current through three has to be equal to the current through six.

06:22 That means the current through number six.

06:24 It's got to be equal to 4 .7 amps.

06:32 And i guess while we're mentioning it, since that current is also going through the battery, that means the current through the battery is 4 .7 amps.

06:43 All right.

06:46 Well, since we're all in this role of, if you have two things, you know the third, well, we just discovered a second piece of information about the battery.

06:56 So if we've got the voltage of the battery, and we divide that by the current, 35 divided by 4 .7 gives us a total resistance or an equivalent resistance of 7 .45 oms.

07:13 So what does that leave us with? let's look at numbers 4 and 5...

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