A battery has an emf ℰ and an internal resistance r . When the battery is connected to a 25-Ωres

A battery has an emf ℰ and an internal resistance r . When...

Key Concepts

Simultaneous Equations

This concept involves solving multiple equations at once in order to determine the values of unknown variables. In circuit analysis, simultaneous equations can be set up when measurements from different configurations of the circuit are available, allowing one to solve for parameters such as emf and internal resistance.

Ohm's Law

Ohm's Law is a fundamental relationship in electrical circuits stating that the current through a conductor between two points is directly proportional to the voltage across the two points and inversely proportional to the resistance. It is used to analyze the behavior of circuits and calculate unknown parameters.

Series Circuit

A series circuit is one in which components are connected end-to-end so that the same current flows through each component. In the context of the battery and load resistor, the internal resistance of the battery and the external resistor form a series circuit, affecting the overall voltage distribution.

Electromotive Force (emf)

This refers to the voltage provided by the battery when no current is drawn from it. It is the energy per unit charge made available by the battery to move charge around a circuit, and is a fundamental characteristic of power sources in electrical circuits.

Internal Resistance

This is the resistance inherent to the battery due to its physical and chemical properties. It causes a potential drop inside the battery when current flows, reducing the terminal voltage compared to the emf, and is important for understanding energy losses in circuits.

Transcript

00:03 Let's consider a scenario in which we have a battery with a certain internal resistance and electromotive force.

00:17 Another unusual looking at me.

00:20 Can't erase right now.

00:22 Secondical issues.

00:28 The fact that the battery is useful information.

00:33 We're not given the electromotive force in strict a sense, but we are told it's the variable.

00:40 Epsilon.

00:43 Same goes for internal resistance, not technically given it.

00:56 We're right an equal sign actually, but i'm overcommitted because i can't always right now.

01:04 We're also told that on external resistance is equal to 25 oms, the current is equal to 0 .665 ampers.

01:29 And that when r2 is equal to 55 oms, the current is equal to 0 .45 .5.

01:45 By ampiers.

01:51 Now, we are commissioned to find the electromotive force.

02:04 I think it would be helpful to review the definition of electromotive force.

02:08 The electromotive force is strictly a term used to refer to, say, some other energy source, say chemical energy.

02:18 That's been transferred into electrical units.

02:25 So it's like chemical energy into voltage.

02:29 But if for our intents and purposes, electromotive force is simply a voltage.

02:37 So whatever you give an electromotive force or a battery, you should consider it as follows.

02:48 Crew drawing of battery.

02:52 So this is the positive side.

02:53 This is the negative side.

02:56 You expect that to correspond to an internal voltage.

02:59 Of course, positive and negative.

03:02 Recalled at the larger end of this symbol, with that symbol in there, it's positive, whereas the smaller end is negative.

03:16 I do believe i forgot something.

03:18 There is an internal resistance.

03:24 We'll call that lowercase r.

03:28 Whereas this voltage, that's the electromagnet of force, or simply epsilon.

03:36 We're asked to consider a circuit in which this battery is connected to a resistor.

03:51 We'll call this uppercase r.

03:58 Now, let's assume the current is going this way.

04:08 In which case, the current goes towards the positive end of the resistor.

04:14 Simply by convention, hopefully the brainwashing has been working for you guys, so you may recall this.

04:25 So we want to find both epsilon and lowercase r, as you recall.

04:30 We are given uppercase r for two different scenarios and the corresponding current...

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