→For the circuit shown in Figure P 28.29, calculate (a) the current in the 2.00-Ωresistor and (b

→For the circuit shown in Figure P 28.29, calculate (a) the...

Key Concepts

Ohm's Law

Ohm's Law relates the voltage (V), current (I), and resistance (R) in a circuit through the equation V = IR. It is a fundamental principle used to calculate the current through a resistor when the voltage across it and its resistance are known, and vice versa.

Kirchhoff’s Voltage Law (KVL)

Kirchhoff’s Voltage Law states that the sum of the potential differences around any closed loop in a circuit must equal zero. This principle is used to establish relationships between the various voltage drops in a circuit, which is essential for determining unknown voltages and analyzing the overall circuit behavior.

Kirchhoff’s Current Law (KCL)

Kirchhoff’s Current Law states that at any junction in an electrical circuit, the total current entering the junction must equal the total current leaving it. This law helps in setting up equations for analyzing current distribution in circuits with multiple branches or nodes.

Resistive Circuit Analysis

Resistive circuit analysis involves methods for simplifying and analyzing circuits composed of resistors. Techniques such as identifying series and parallel resistor combinations are used to calculate equivalent resistances, which in turn facilitate the determination of individual currents and voltage drops within the circuit.

Transcript

00:01 Okay, so we have this configuration and we want to find what is the current in the 2 -1 resistor and then what is the potential difference between points a and b.

00:12 Okay, so the first thing we have to do is draw the currents.

00:18 So we are going to start, remember that the large bar means positive, the small one negative.

00:26 Okay, here this is the large and this is the small one.

00:30 Okay, and you will see that normally current flows from negative to positive terminal.

00:39 This can change.

00:40 The important thing is you keep it the same for all your calculations.

00:45 So i'm going to have that this is i -1.

00:48 So i -1 comes through here, it gets to this point and divides.

00:53 One part of i -1 comes through here.

00:57 I'm going to call this i -2.

00:58 And one comes like here down towards to the to worm resistor and this is i3 so basically i want to find it i3 and for this i i am going to use these rules okay this will help me to find three equations i have three currents unknown and from this i can solve for i3 okay so the first one is if we actually look into this point, okay? i'm going to see that for the joint law, i know that i, 1 must be equal to i2 plus i3, okay? and this is the first equation.

01:49 The second equation is i'm going to use the loop rule, that is the second rule that is there.

01:56 And for this rule, i'm going to choose just.

01:59 This loop up and going counter -cloakwise okay and this is important remember that the the pendant it does not matter the direction you take it because the signs will change okay so when you take the voltage from negative to positive okay it is a positive voltage and when you take the current when you're measuring or taking the circuit in the same sense of the current.

02:32 This will be negative.

02:35 The voltage will be negative.

02:39 And the contrary case of both is the opposite sign.

02:43 So for this look, i start in the 12 volts.

02:47 Since i'm going to negative to positive, this is positive.

02:51 Then i get to the 2 -on resistor.

02:56 I have 3 in the same direction that i'm moving.

03:00 So this is minus 2 times i3.

03:04 This is because since i don't know the exact value of the potential difference, i know that this is the value of the resistor times the current known.

03:14 So i know the resistor and i do not know this.

03:17 And then i go upwards to the 4 -hom resistor and the same is negative and i have 4 times i won.

03:28 Okay, i 1 because in this point all the currents meet, i 2 and i3 and this becomes i 1.

03:35 So this must be equal to 0.

03:39 And i'm going to rearrange in terms of i3.

03:44 Why? because the one that i want to find is i3, that is the one in the 2 -1 resistor...

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