Find the current through each of the three resistors of the circuit shown in Fig. P26.61. The em

step 1 So here we have the circuit and these are the two voltage sources. In fact, the three voltage so

Find the current through each of the three resistors of the...

Key Concepts

Ohm's Law

Ohm's Law is the fundamental relationship between voltage, current, and resistance in an electrical circuit, mathematically expressed as V = IR. It serves as the basis for understanding how the electrical energy is distributed across components, allowing one to calculate the current through a resistor when the voltage across it and its resistance are known.

Kirchhoff's Circuit Laws

Kirchhoff's Circuit Laws, including Kirchhoff's Voltage Law (KVL) and Kirchhoff's Current Law (KCL), are essential for analyzing circuits with multiple components. KVL states that the algebraic sum of all voltages in any closed loop is zero, while KCL asserts that the total current entering a junction must equal the total current leaving it, both of which are critical for setting up equations to solve for unknown currents and voltages in circuits.

Series and Parallel Resistor Combinations

Understanding series and parallel resistor combinations is crucial for circuit analysis as it enables the simplification of complex circuits. In series configurations, resistances add directly to find the total resistance, whereas in parallel configurations, the total resistance is found by taking the reciprocal of the sum of the reciprocals of the individual resistances. This concept helps in reducing the circuit to a simpler equivalent circuit for analysis.

Mesh and Node Analysis Techniques

Mesh analysis and node analysis are systematic methods used to solve for unknown currents and voltages in complex circuits. Mesh analysis involves applying Kirchhoff's Voltage Law to the independent loops of a circuit, while node analysis uses Kirchhoff's Current Law to analyze the currents at the nodes of a circuit. These techniques enable one to derive a set of simultaneous equations that can be solved to determine the state of every component in the circuit.

Transcript

00:01 So here we have the circuit and these are the two voltage sources.

00:05 In fact, the three voltage sources.

00:08 And we need to figure out the current flowing through each of these resistors involved in this connection.

00:18 So let us take the tentative direction.

00:21 And here i can, before that, combine these two emf sources.

00:27 So i just shift this emf and we can see the positive terminals are connected together.

00:32 So the effective emf here will be 6 volt and this is 2 oom resistor and we have this connected with this 4 -on resistor and here we have 5 -oam and connected to this 36 -volt battery.

01:00 So we have obtained this 6 -volt because positive terminals are connected, 20 minus 14, that will be 6 -volt.

01:08 So let us redraw the circuit even more clearly.

01:13 So we have this 36 volt battery and there is 5 -on resistor here.

01:25 Here also we have the 2 -oom resistor and let's again shift the position to make it look symmetrical.

01:33 So we have 6 volt battery like this.

01:39 This is 6 volt and these are connected and they are connected across this 4 -oom.

01:45 Resistor.

01:48 So here to find out the current that is flowing through each of these resistors, first this battery.

01:56 So let us take the potentials at all these points.

02:00 So it will be zero.

02:02 And here the potential will be 36.

02:07 And here the potential will be minus 6.

02:10 And let us take the potential here to be v.

02:13 So once we find out we, we can figure out the current that is flowing through all the resistors.

02:20 So let's take any junction into consideration.

02:23 So let's say i take this junction.

02:27 So at this junction, let us take the directions of current.

02:33 So this is the current.

02:35 And here, this is the current.

02:37 And this is the current.

02:39 So let's take this as i1.

02:41 This is i2 and this is i3.

02:43 So if you apply kirchop's current law here, total current entering this junction is i1...

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