The circuit considered in Problem 21 and shown in Figure P28.21 is connected for 2.00 min. (a) F

step 1 Okay, so this problem is just a continuation of problem 21. Okay, in that problem, we already fo

The circuit considered in Problem 21 and shown in Figure...

Key Concepts

Energy Transformation and Conservation in Circuits

This concept covers the various forms of energy conversion and the application of the conservation of energy principle in electrical circuits. In a circuit, energy is transformed from one form to another – for example, chemical energy in the battery is converted into electrical energy, which is then partly transformed into thermal energy in resistors. Understanding this ensures that the total energy delivered by the battery equals the sum of the energies transformed in all circuit elements, thereby adhering to the law of conservation of energy.

Time-dependent Energy Calculations

The analysis of energy in circuits often involves calculating the energy over a specific time interval. This concept focuses on integrating power over the time during which a circuit operates to determine the total energy transferred or dissipated. It is crucial when circuits are connected for a finite time, as the energy delivered by sources and dissipated by resistive components is directly proportional to the duration of operation.

Electrical Energy Delivery by Batteries

This concept involves calculating the energy supplied by a battery when it provides a voltage over a certain time period. It includes understanding that a battery converts stored chemical energy into electrical energy, and the energy delivered is typically the product of the battery’s voltage, the current it supplies, and the time for which the circuit is active. This principle is central to energy analysis in circuits, where the battery’s performance is quantified by the amount of energy it imparts to the circuit components.

Energy Dissipation in Resistors

Resistors in a circuit convert electrical energy into heat through a process known as Joule heating. The key idea here is that as electric current passes through a resistor, energy is lost in the form of thermal energy due to the resistance to the flow of electrons. This concept involves using power formulas such as P = I²R or P = V²/R, and then integrating power over time to find the total energy dissipated.

Transcript

00:01 Okay, so this problem is just a continuation of problem 21.

00:05 Okay, in that problem, we already found the values of the currents, which are here in red.

00:13 And for this part, we have to find what is the energy of the battery and the resistors, and what are the energy transformations in this kind of configuration.

00:25 Okay, so we just have to use these relationships to energy and current, the resistor value of the time.

00:35 And we can also use this other one, and it's actually the ones we have to use for the battery because there is no value of the resistors.

00:45 If you remember omnslaw, you can just substitute this in here, and you have energy in terms of potential difference.

00:55 Okay? and we have to use the time in second, so we can be consistent in the units.

01:04 Okay, so for the first part, as i said, we have to use that energy equals the current times the potential difference times the time.

01:13 Okay, and then for the 12 -vote battery, the one we have here.

01:20 Okay, this is just the current.

01:23 I know the value of the current is the one point and 31 ampere times the potential difference, times the time.

01:31 Okay, so if you make this calculation, this is 1 ,886 u, which you can just say is 1 .88 kilo -u if you make the, if you want to make the unit conversion.

01:46 And for the fourth volt battery is the one that we have here, okay? this is kind of tricky because we have other currents.

01:55 We have the 0 .462 amp.

02:00 But here we have it flowing from positive to negative.

02:07 Okay, in the other battery it was flowing from negative to positive.

02:11 So this is a, let's say, a positive current.

02:15 And in this case, in the other case, from positive to negative, is going to be a negative current.

02:21 Okay, so i'm going to use the minus 0 .462 ampers times the potential difference, which is 4.

02:30 And times the time.

02:32 If you make this calculation, this is minus 221 .7 joules, which you can just round up to minus 222.

02:44 Okay, so these two are the answers for the energy in the batteries.

02:50 And now i'm going to calculate what are the energy in each of the resistors...

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