For the circuit shown in Figure P 28.25 , calculate (a) the current in the 2.00-Ωresistor and (b

For the circuit shown in Figure P 28.25 , calculate (a) the...

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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 So we have a circuit here where we're trying to find the current that's running across this 2 -home resistor, and we also want to find the potential difference between point a and point b.

00:12 So the way that we're going to do that is we're going to apply the loop rule and the junction rule in order to set up a system of equations where we can then solve for the unknown.

00:23 So we're going to do first is we're going to apply the loop or the junction rule to this point right here.

00:29 So we'll take notice of which current is coming in, so we can see i3 and i2 coming into the junction, and we have i1 coming out.

00:39 So we can write this as our first equation, as i1 is equal to i2 plus i3.

00:49 So now what we can do for a second equation is apply the loop rule.

00:54 And we're going to use this top loop first, and we're going to go counterclockwise, starting at the 12 -volt battery.

01:02 So our equation should look like this.

01:04 We'll have 12 minus 2 times i3.

01:08 And we have a minus here because we're going across the resistor in the direction of the current as it's drawn.

01:15 We'll then have minus 4 times i1 equal to 0.

01:22 And now doing the same going counterclockwise in this bottom loop here.

01:28 We'll have 8 minus 6 times i2 plus 2 times i3.

01:37 And we'll set that equal to zero...

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