Find the current in each of the resistors in the circuit shown in Figure 5.29 . What is the tota

step 1 In this question, we have this circuit. So we have a battery with 12 volts DMF, 3 oom internal r

Find the current in each of the resistors in the circuit...

Key Concepts

Ohm's Law

Ohm's Law describes the relationship between voltage, current, and resistance in an electrical circuit. It is expressed as V = I × R, where V is the voltage across a resistor, I is the current flowing through it, and R is the resistance. This law is fundamental for determining the current in circuit components when the voltage and resistance are known.

Kirchhoff's Circuit Laws

Kirchhoff's Circuit Laws consist of two main rules: Kirchhoff's Current Law (KCL) and Kirchhoff's Voltage Law (KVL). KCL states that the total current entering a junction equals the total current leaving the junction, while KVL states that the sum of the electrical potential differences around any closed circuit loop must be zero. These laws are essential for analyzing complex circuits and determining currents and voltages in various branches.

Equivalent Resistance

Determining the equivalent resistance in a circuit involves combining resistors that are arranged in series or parallel. For series combinations, resistances are added directly, while for parallel combinations, the reciprocal of the equivalent resistance is the sum of the reciprocals of each resistance. Calculating the equivalent resistance simplifies complex resistor networks into simpler forms for easier current and voltage analysis.

Power Dissipation in Resistors

Power dissipation in resistors refers to the conversion of electrical energy into heat within the resistor, and it can be calculated using formulas such as P = I² × R, P = V² / R, or P = I × V. Understanding power dissipation is crucial for ensuring that circuit components can handle the thermal energy generated during operation and for evaluating the overall energy efficiency of the circuit.

Transcript

00:01 In this question, we have this circuit.

00:04 So we have a battery with 12 volts dmf, 3 oom internal resistance.

00:11 Then the external resistors are 60 oms, 57 oms, then we have 40 oms, 20 ooms, and here 60 oms.

00:31 Okay, so we want to find a current in each of the resistors and the total power dissipated in the circuit okay, so first thing we need to do is to simplify the circuit okay or we draw the circuit so so we have this 40, 20 om and a 60 om combination okay, so this is equal to 60 oms and 60 oms combination and then this is equal to 30 ome combination but 30 own resistor okay right so the circuit we're drawing the circuit okay this is what we get 60 oms 57 oms this is 3 oms and then another 30 oms resistor okay okay, so with this diagram, you can tell the total resistance easily.

02:09 So our total is equal to 60 plus 57 plus 30 plus 3.

02:16 And it is 150 oms.

02:19 So the current in the circuit is equal to e divided by r total, 12 by 150.

02:33 So the answer is 0 .08, 0 ampers, okay? alright, so then we can go back to the diagram.

02:52 So we know that this is 0 .8 ampers, then when it comes to here, it will split into 2, 0 .4m and 0 .4ms, because the top branch and the bottom branch, they have the same resistance.

03:09 And then combine back to 0 .8 ampers.

03:14 So the, okay, so i'm going to label the circuits, or the resistors, r1, r2, r3, 4, r5, and then this is more rk.

03:48 So the current i1, i1 equals to i2, it goes to 0 .5...

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