Consider the circuits shown below. (a) What is the current through each resistor in part (a)? (b

Consider the circuits shown below. (a) What is the current...

Key Concepts

Ohm's Law

Ohm's Law is a foundational principle in electrical circuit analysis that establishes a direct relationship between voltage, current, and resistance. It states that the voltage across a resistor is equal to the product of the current flowing through it and its resistance. This law serves as the basis for calculating currents and voltages in various parts of a circuit, which is essential when determining the performance of individual components and overall circuit behavior.

Kirchhoff's Circuit Laws

Kirchhoff's Circuit Laws comprise Kirchhoff's Current Law (KCL) and Kirchhoff's Voltage Law (KVL). KCL states that the sum of currents entering a junction equals the sum of currents leaving it, reflecting the conservation of charge. KVL asserts that the sum of all voltage drops in a closed loop must equal the total applied voltage, ensuring energy conservation. Together, these laws are critical for analyzing complex circuits by forming the equations needed to solve for unknown currents and voltages.

Series and Parallel Circuits

Understanding series and parallel circuits is crucial because the arrangement of resistive elements determines how current and voltage are distributed in a circuit. In a series circuit, components are connected end-to-end, so the same current flows through each resistor, but the voltage drop is divided among them. In contrast, parallel circuits allow multiple paths for current, resulting in the same voltage across each branch while the total current splits among paths. Recognizing these configurations helps in setting up the proper equations for circuit analysis.

Power in Electrical Circuits

Power calculation in electrical circuits involves determining how much energy is consumed or dissipated by a component, which is especially important for evaluating circuit performance and safety. Power can be calculated using formulas such as P = I²R (where power is proportional to the square of the current and resistance) and P = V²/R (where power is related to the square of the voltage divided by resistance). Understanding these relationships helps in assessing how resistors and other components manage energy within both supply and consumption contexts.

Transcript

00:01 For this question we are given two different circuits, which i have labelled as a and b.

00:07 So a is the circuit at the top and b is the circuit below.

00:10 They have the same similar batteries as well as similar resistors in the same positions.

00:19 But the only difference is that the direction of a battery for v2 is different.

00:26 It is swapped over between a and b.

00:31 We're going to see how this affects our current.

00:36 So first off, we're going to assume the direction of the current.

00:41 Alright, that is for a.

00:47 We're going to solve for a first.

00:49 I'm going to assume this is current i1, since it passes through resistor 1.

00:55 And in this junction, going to assume that the current flows in this direction.

01:00 This will call i2 and over here i'm going to assume that it is flowing in this particular direction i'm going to call this i3 so from this junction over here this junction we use kutchev's rule we should be able to get a equation right that will be i1 plus i3 goes to i2 next, we're going to use the kirchhoff's rule to look at different loops in our circuits.

01:48 And we're going to use these two loops.

01:50 So the first loop is anti -clockwise.

01:55 This is a clockwise direction on the left -hand side, right, for the small loop.

02:04 And then we're going to look at the large clockwise direction but for the outer loop.

02:11 So these two loops so for the first loop we have passing through the battery we have v1 then it passes through r1 in the same direction as the current so we get r1 i1 so it minus away r1 i1 then it passes through r2 with the same direction again so that's r2 i2 get this to 0 by of through the third equation we're going to get would be the outer loop which first we pass through the battery in the right direction so that we add up the potential difference so that's v1 then we pass through v2 but in the wrong direction right from plus to minus so we must subtract away v2 then we pass through r3 with i3 in the same direction as the current that we assign.

03:19 So that will be r3, i3.

03:25 Then next we pass through r2.

03:29 So that's r2, i2.

03:32 Create that to 0.

03:34 So now over here we have three unknowns, i2, i3, and i1, with three equations.

03:42 We should be able to solve this simultaneous equations.

03:48 So one of the way is to reassign i2.

03:55 Right, i2, we already know it's equal to i1 plus i3...