There is a current of 0.25 A in the circuit of FIGURE...

Key Concepts

Power Dissipation

Power dissipation in a circuit component, such as a resistor, refers to the rate at which electrical energy is converted into heat. It is calculated using formulas like P = I^2R or P = VI. Understanding power dissipation is essential for ensuring that components can handle the energy conversion without damage and for evaluating the efficiency of a circuit.

Kirchhoff's Voltage Law

Kirchhoff's Voltage Law (KVL) states that the sum of all electrical potential differences around any closed loop in a circuit is zero. This principle is used to analyze and determine voltage drops and gains across various components in a circuit, often visualized through potential versus position graphs that map the changes in voltage throughout the circuit loop.

Ohm's Law

Ohm's Law is a fundamental principle in electrical circuits that relates voltage (V), current (I), and resistance (R) with the equation V = IR. This relationship allows one to calculate any one of these quantities if the other two are known, thereby serving as a cornerstone for analyzing the behavior of electrical circuits.

Resistance

Resistance is a measure of how much a component or material opposes the flow of electric current. It is measured in ohms (?) and affects the current in a circuit according to Ohm’s Law. In circuit problems, determining resistance involves understanding its role in converting electrical energy into other forms, such as heat, and calculating it using voltage and current relationships.

Electric Current

Electric current is the flow of electric charge, typically measured in amperes (A). It defines the movement of electrons through a conductor and determines how much charge passes a given point per unit of time. In circuit analysis, the direction of current flow is conventionally taken from the positive terminal to the negative terminal, regardless of the actual electron flow direction.

Transcript

00:01 Now in this question we have this circuits and the first thing i want to do is to identify the direction of the current.

00:07 Now the batteries in this case are kind of like opposing each other, right? they are attached from plus end to the plus end.

00:19 And the current will actually flow in the direction of the plus sign of the battery, but only depending on which battery has a greater voltage.

00:28 So for the 12 volts, this is a larger, voltage than the 6 volts, so we expect the current, overall current to be pointing from the positive end of the 12 volt battery, which is the higher voltage battery.

00:46 So we expect the current to flow in the counter clockwise direction.

00:54 Now the second part we want to find the resistance are of this resistance.

01:02 So we're going to use kachov's loop rule and we're going to go in the counter clockwise direction.

01:08 Starting from the bottom right hand side corner.

01:15 So the first part we move past the battery from minus to plus n, so we'll add the emf, it's 12 volts.

01:24 We move past the 12 oom resistor in the same direction as the current, so we'll subtract away the potential drop, which will be the currents multiplied by the resistance.

01:37 Now give it that the current is 0 .2 .2.

01:39 0 .25 amps.

01:42 This is shed among all the components because it's a series circuit.

01:47 So it's just take 0 .25 multiple by 12.

01:50 Reto the same for a 6 ome resistor because it's moving same direction as the current.

02:00 Then we bypass the 6 volt battery but from plus to minus.

02:05 So we have to subtract away the emf.

02:07 6 volts.

02:08 Finally we reach the unknown resistor.

02:12 Subtray away the potential drop.

02:13 Which is your 0 .25 times r.

02:18 And then we equate this to 0.

02:25 So bringing the term with the r to the right hand side, and then we leave the rest of the terms here, and then we're going to try to simplify this, right? so 0 .25 times 12 is 3.

02:37 So 12 volts minus 3.

02:40 0 .25 times 6, it's about 1 .5, minus 1 .5 minus 6 volts.

03:04 So our r resistance is just 1 .5 divided 0 .25 which is 6 oms.

03:16 To find the power dissipated by this resistor we can use the equation i square r...

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