A dead battery is charged by connecting it to the live battery of another car with jumper cables

A dead battery is charged by connecting it to the live...

Key Concepts

Battery Charging

Battery charging refers to the process of replenishing the energy stored in a battery by applying an external voltage source. The charging process depends on the battery's state of charge, its internal resistance, and the characteristics of the charging source. Proper analysis of the charging circuit ensures that the battery receives the appropriate current and voltage without being damaged.

Circuit Analysis

Circuit analysis involves applying fundamental principles, such as Kirchhoff's laws, to determine the distribution of currents and voltages throughout an electrical network. It requires setting up and solving equations based on the conservation of energy and charge, which is essential for understanding how different components in a circuit interact, especially when dealing with multiple power sources or branches.

Kirchhoff’s Laws

Kirchhoff's laws, including the voltage law (KVL) and the current law (KCL), are fundamental in circuit analysis. KVL states that the sum of the voltages 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 principles are essential for calculating currents and voltages in circuits with multiple loops or nodes.

Battery Internal Resistance

Battery internal resistance is the resistance within a battery that impedes the flow of current. It plays a critical role in battery operation and charging since the voltage drop across the internal resistance reduces the effective voltage available to drive current through a circuit. Understanding internal resistance is crucial for accurately determining charging currents and overall battery performance.

Current Distribution in Series and Parallel Circuits

Current distribution in circuits involves determining how electrical current divides among different branches, particularly in series and parallel configurations. In analyzing such circuits, one must consider the resistances offered by various components, including cables, batteries, and motors, to compute the current flowing through each part of the circuit accurately.

Transcript

00:03 Okay, so we want to know what the current is the starter and the dead battery is.

00:09 Okay, so the first thing i have to do know is that draw the current.

00:15 So i know that generally current goes from negative to positive.

00:21 Okay, this is for i1.

00:23 Okay, it comes through this point and it's going to divide.

00:27 Okay, i'm going to have i2 from here and and the other one i'm going to call i3.

00:36 Okay, and i'm going to use two rules.

00:43 One is the junction rule.

00:46 You must be familiar with it.

00:49 It tells that the sum of the currents that come in in a junction equals the sum of the current that go out of the junction.

00:59 And the other is the loop rule that tells that the sum of all the potential differences in a closed look was equal to zero.

01:09 So with these two equations, i'm just going to establish two or three equations, okay, to solve the circuit and find the currents.

01:23 Okay, so the first one i'm going to see the junction rule in this point.

01:30 Okay, so you see it's pretty easy.

01:32 It comes current 1 through here and it divides in the current 2 and current 3 okay so remember this is current 3 i just put okay and so i 1 must be equal to i 2 plus i 3 for the junction rule to be 2 be 2 okay so this is the first equation for the other questions i'm going to use the closed loop rule and i'm going to look at two different loops okay the first one is starting at 12 volts from here and is the loop that goes all the way the circuit okay we go back here okay so remember when i take i'm moving uh in the clockwise direction okay so when i measured or take a voltage from minus positive it's positive okay so i start into 12 volts so this is 12 positive okay then i get to the 0 .01 um resistor if you see we are moving in the same direction as the current here so this value must be negative okay the value of the potential difference here and i don't know it exactly but i know on slow that says that voltage equals resistor value times the current.

03:11 Okay, so this is the resistor value 0 .01 times the current and this is i1.

03:20 Okay and then i get to this 0 .06 resistor.

03:25 You see actually this is the same direction as the current so it's negative and is the resistor value times the current that this time is height 3.

03:36 So this will be equal 0, and this is my second equation.

03:41 And the other one i'm going to use dark blue.

03:49 Now i already use that purple.

03:52 Okay, and is this small loop that goes...

03:56 Sorry, i already use purple.

03:59 I'm using this pink.

04:02 I hope it gets different.

04:04 I'm going to take this small loop in the same direction.

04:08 That is a clockwise direction.

04:11 And i start in the 10 volts voltage since it's from negative to positive.

04:19 It's positive.

04:22 And i get to the one arm resistor.