In the circuit shown in the figure, R1=3.00 ΩR2=6.00 Ω, R3=20.0 Ω, and Vemf=12.0 V a) Determine

In the circuit shown in the figure, R1=3.00 ΩR2=6.00 Ω,...

In the circuit shown in the figure, $R_{1}=3.00 \Omega$ $R_{2}=6.00 \Omega, R_{3}=20.0 \Omega,$ and $V_{\mathrm{emf}}=12.0 \mathrm{~V}$ a) Determine a value for the equivalent resistance. b) Calculate the magnitude of the current flowing through $R_{3}$ on the top branch of the circuit (marked with a vertical arrow)

In the circuit shown in the figure, $R_{1}=3.00 \Omega$ $R_{2}=6.00 \Omega, R_{3}=20.0 \Omega,$ and $V_{\mathrm{emf}}=12.0 \mathrm{~V}$
a) Determine a value for the equivalent resistance.
b) Calculate the magnitude of the current flowing through $R_{3}$ on the top branch of the circuit (marked with a vertical arrow)

Key Concepts

Equivalent Resistance

Equivalent resistance is the single resistance that can replace a combination of resistors in a circuit without affecting the overall current and voltage characteristics. It simplifies circuit analysis by reducing complex resistor networks into a single resistor value, allowing easier calculations using Ohm's law or other circuit principles.

Series and Parallel Resistor Combinations

Understanding series and parallel resistor combinations is fundamental to circuit analysis. Resistors in series combine by summing their resistances, while resistors in parallel combine according to the reciprocal sum of their individual resistances. Recognizing these configurations is crucial for determining the overall resistance of a circuit and for further application of current and voltage distribution principles.

Ohm's Law

Ohm's Law is a basic principle in electrical circuits that relates voltage (V), current (I), and resistance (R) through the equation V = IR. It is essential for calculating the current or voltage drop across circuit elements when the resistance is known, and it serves as the foundation for analyzing and designing electrical circuits.

Current Division

The current division principle is used to determine the distribution of current among parallel branches in a circuit. When resistors are arranged in parallel, the total current splits inversely proportional to the resistance of each branch. This concept is vital for accurately calculating the current flowing through individual circuit elements in parallel networks.

Transcript

00:01 In this given problem there is a complicated looking circuit diagram which is comprising of the source of emf having vemf as its value then in the upper circuit in the upper branch of this circuit there are two resistors in parallel combination these two are having the values r1 and r2 then r3 is in series with them and then again r1 and r2 again in parallel combination then the circuit is closed and one identical loop below this source of emf the two resistors in parallel r1 r2 one in series r3 and then again the same two resistors in parallel r1 and r2 and again the same two resistors in parallel r1 and r2 and again the lower loop is closed now the values of these resistors are r1 is 3 .00 om, r2 is 6 .00 om, r3, that is 20 .00 om.

01:41 And the value of emf, that is 12 .0.

01:48 Now in the first part of the problem, we have to find equivalent resistance of the this combination.

01:55 So as these r1 and r2 are in parallel combination, so we can say them to be rp, the net resistance of this parallel combination rp and this will also be rp.

02:11 So first of all, as these two loops are identical, so first of all we will find the resistance of this upper branch and it will be similar to that of the lower branch and these two branches are in parallel now as r1 and r2 are in parallel so their net resistance is given as let it be r p so this is given by the product of the two resistors in numerator and their addition in denominator this is the root if we have to add just two resistors in so for r1 this is 3 .00 om for r2 this is 6 .00 ome divided by 3 .00 plus 6 .00 om.

03:14 Then canceling this one om r p comes out to be 0 .00 om and as there are two parallel combinations the similar identical parallel combinations.

03:33 The net resistance of upper in which all the three resistors are in series.

03:49 So we name it as rs.

03:53 So it will be rp plus r3 plus one more rp.

03:58 This is 2 .00 plus 20 .0 plus 2 .00 ome.

04:07 And here it will come out to be 24 .0 om...

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