Consider the circuit shown in Figure P28.9. Find (a) the current in the 20.0-Ωresistor and (b) t

Consider the circuit shown in Figure P28.9. Find (a) the...

Key Concepts

Voltage Divider Principle

The voltage divider principle is a useful concept for determining the voltage across a particular resistor in a series circuit. It states that the voltage across a resistor is proportional to its resistance relative to the total resistance in the series. This concept is particularly useful when needing to find the potential difference between two points in a series network, as it directly relates the resistor values to the voltage distribution.

Ohm's Law

Ohm's Law is a fundamental principle in electrical circuits that relates voltage (V), current (I), and resistance (R) through the equation V = IR. This law is essential for predicting the behavior of circuits, allowing one to calculate the potential difference across an element if the current and resistance are known, or vice versa.

Kirchhoff's Circuit Laws

Kirchhoff's Circuit Laws, which include the Voltage Law (KVL) and the Current Law (KCL), are critical for analyzing complex circuits. KVL states that the sum of potential differences around any closed loop in a circuit must equal zero, while KCL asserts that the total current entering a junction must equal the total current leaving it. These laws help in setting up equations that govern the flow of current and the distribution of voltage in a circuit.

Series and Parallel Resistor Networks

Understanding series and parallel resistor networks is key to circuit analysis. In a series configuration, resistors add directly, affecting the overall resistance and current flow. In parallel configurations, the inverse of the total resistance is the sum of the inverses of the individual resistances. Recognizing these arrangements allows for the simplification of complex circuits into more manageable equivalents, facilitating easier computation of voltage and current.

Transcript

00:01 So we are given these circuits and we want to know what is the current in this resistance and what is the potential difference in the points a and b.

00:15 Okay, so this one is actually it's not hard, it's just tricky.

00:22 Okay, so i redraw the circuit here so we have more clarity and it's having to solve it.

00:31 So you can see we have here the difference in potential and we have this resistance of 10 um in series with these ones.

00:44 Okay, i'm just going to draw all of these ones that are in parallel.

00:49 Okay, so this is in series with all of this.

00:53 So the first thing we have to do is simplify this.

00:57 Okay, so we can find, we can, come through this and see what is the total current in all the circuit.

01:06 Okay, so the first step and actually when you see this, you see that the potential difference is actually between these two resistance.

01:16 But it's easier than it looks because you know that the potential difference actually in all of this because they are in parallel is going to be the same.

01:27 Okay.

01:27 So the first thing we have to simplify is these two.

01:32 Since these are in series, we know that the total resistance for this two is going to be the sum of both of the resistance.

01:43 Okay, so this is going to be actually 25 on.

01:46 So this one here is 25 on.

01:49 I draw this already so it's like less time so.

01:54 Okay, and then in a green column.

01:57 Then we are going to simplify these three resistance that are the ones that are in parallel between them and in series with this so when we simplify it will look like this okay this is this one and since this is in parallel we have to find one and dividing the total resistance of this in parallel it's going to be one over 25 plus 1 over 5 plus 1 over 10 this is going to be uh 1 i'm sorry 17 over 50 you can actually do the map so when i shift this okay remember if i shift this i shift this so 50 over 17 and this is actually 2 .94 um okay so this one simplification to this and the value is 2 .94 on okay and then we'll do this color we just simplify this too so since these are in series i just have to follow the total resistance okay so the total resistance i'm sorry the total resistance is going to be 10 plus 2 .94 on this is actually going to be 12 .94 on...

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