Consider the circuit in the drawing. Determine (a) the magnitude of the current in the circuit a

Consider the circuit in the drawing. Determine (a) the...

Key Concepts

Ohm's Law

Ohm's Law is a foundational principle in electrical circuits stating that the voltage across a resistor is directly proportional to the current flowing through it, with resistance being the constant of proportionality. This law is used to calculate one of the three variables—voltage, current, or resistance—when the other two are known.

Kirchhoff’s Circuit Laws

Kirchhoff’s Circuit Laws, which include Kirchhoff’s Voltage Law (KVL) and Kirchhoff’s Current Law (KCL), are essential for the analysis of electrical circuits. KVL states that the sum of the electrical potential differences around any closed loop is zero, while KCL states that the total current entering a junction must equal the total current leaving the junction. These principles are critical for determining unknown values such as current magnitudes and node voltages in complex circuits.

Node Voltage Analysis

Node Voltage Analysis is a systematic method used to determine the voltage differences between nodes in an electrical circuit. By assigning potential values to key points in the circuit and applying Kirchhoff’s Current Law and Ohm’s Law, one can solve for unknown node voltages, which is useful in determining the voltage between specific points in the circuit.

Series and Parallel Circuit Analysis

Series and parallel circuit analysis involves understanding how resistors and other components combine to affect overall circuit behavior. In a series circuit, components have the same current flowing through them, while in a parallel circuit, the voltage across each component is the same. This concept is important for evaluating equivalent resistance and using it to determine current distribution and voltage drops in a circuit.

Transcript

00:01 Okay, in this question, we're going to use kirk -off loop rule to determine various characteristics of a circuit.

00:07 A circuit we're given has four resistors in it, various resistances, and two batteries.

00:15 So in question a, they ask us, what is the magnitude of the current? so we can use v -equals ir to solve this.

00:29 So this is a little bit confusing since we have two different voltages and they're pointed in different directions.

00:37 So we can also solve this using, or we can also look at this kirk -off's loop rule, which we'll see is the same thing.

00:47 But it will make it a little bit more clear how to consider the voltages.

00:52 So the kirk -off's loop rule says that if you make a complete loop in a closed circuit, the sum of the voltage gains and drops will be equal to zero.

01:03 Alright, so let's count up all those drops and make sure they're equal to zero.

01:10 So zero is going to be equal to the gains will come from the batteries if they're going in the same direction, if they're pointing the same direction that the current is flowing and all the drops will occur from resistors and any batteries that are pointing opposite to the direction in the current.

01:30 So first we're going to have to determine the direction of the current.

01:33 It's going to be going to this way, since this battery is more powerful than this one.

01:39 So starting at point a, let's make our week and consider all the gains and drops.

01:44 So we're going to have a gain of 30 volts and a drop, so i'm adding a negative sign, of the current times r27, i'll call mixed resistor.

01:58 And then we're going to have another drop of 10.

02:02 This is a drop because it's pointing opposite the direction of the current.

02:05 And then another drop of ir12, another drop of ir8, and another drop of i r5.

02:18 And we're back to point a.

02:20 So all of these should come up to zero.

02:23 And we can start combining terms.

02:27 So we're going to have 30 minus 20 is, or 30 minus 10 is 20.

02:34 Which is going to be equal to, i'm just going to add all the drops across the resistors to the other side.

02:40 So we're going to have i times r27 plus r12 plus r8 plus r5.

02:52 And you'll notice this is just v equals ir.

02:55 This is our voltage, what's left after some of it was canceled out...

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