By loop, I mean any path traced from one point in a circuit around to other points in that circuit, and finally back to the initial point. If we were to take that same voltmeter and measure the voltage drop across each resistor , stepping around the circuit in a clockwise direction with the red test lead of our meter on the point ahead and the black test lead on the point behind, we would obtain the following readings: We should already be familiar with the general principle for series circuits stating that individual voltage drops add up to the total applied voltage, but measuring voltage drops in this manner and paying attention to the polarity mathematical sign of the readings reveals another facet of this principle: that the voltages measured as such all add up to zero: In the above example, the loop was formed by the following points in this order: This is because the resistors are resisting the flow of electric charge being pushed by the battery. Here we see what a digital voltmeter would indicate across each component in this circuit, black lead on the left and red lead on the right, as laid out in horizontal fashion: If we were to take that same voltmeter and read voltage across combinations of components, starting with the only R1 on the left and progressing across the whole string of components, we will see how the voltages add algebraically to zero : The fact that series voltages add up should be no mystery, but we notice that the polarity of these voltages makes a lot of difference in how the figures add.

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This law is also known as Point Law or Current law. In any electrical network , the algebraic sum of incoming currents to a point and outgoing currents from that point is Zero. Or the entering currents to a point are equal to the leaving currents of that point. In other words, the sum of the currents flowing towards a point is equal to the sum of those flowing away from it. Or the algebraic sum of the currents entering a node equals the algebraic sum of the currents leaving it.

In other words, in any closed loop which also known as Mesh , the algebraic sum of the EMF applied is equal to the algebraic sum of the voltage drops in the elements. The overall sum of E. The imaginary direction of current is also shown in the fig. E1 drive the current in such a direction which is supposed to be positive while E2 interfere in the direction of current i. The voltage drop in this closed circuit is depends on the product of Voltage and Current.

The voltage drop occurs in the supposed direction of current is known as Positive voltage drop while the other one is negative voltage drop.

If we go around the closed circuit or each mesh , and multiply the resistance of the conductor and the flowing current in it, then the sum of the IR is equal to the sum of the applied EMF sources connected to the circuit.

The direction of current can be supposed through clockwise or anticlockwise direction. Once you select the custom direction of the current, you will have to apply and maintain the same direction for over all circuit until the final solution of the circuit. If we got the final value as positive, it means, the supposed direction of the current were correct. In case of negative values, the current of the direction is reversal as compared to the supposed one then.

Find the current through each resistor. Solution: Assume currents to flow in directions indicated by arrows.



Example 1: Find the three unknown currents and three unknown voltages in the circuit below: Note: The direction of a current and the polarity of a voltage can be assumed arbitrarily. To determine the actual direction and polarity, the sign of the values also should be considered. For example, a current labeled in left-to-right direction with a negative value is actually flowing right-to-left. All voltages and currents in the circuit can be found by either of the following two methods, based on KVL or KCL respectively. The loop-current method mesh current analysis based on KVL: For each of the independent loops in the circuit, define a loop current around the loop in clockwise or counter clockwise direction.


Kirchhoff's Laws



kirchhoff’s law


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