kirchhoff's voltage law exercises

Kirchhoffs postulated two basic laws way back in 1845 which are used for writing network equations. These laws concern the algebraic sum of voltages around a loop and currents entering or leaving a node. The word algebraic is used to indicate that summation is carried out taking into account the polarities of voltages and direction of currents. While traversing a loop we will take voltage drops as positive and voltage rises as negative. Also while considering currents at a node, the currents entering the node will be taken as positive and those leaving would be taken as negative.

Kirchhoffs voltage law usually abbreviated as KVL is stated as follows : The algebraic sum of all branch voltages around any closed loop of a network is zero at all instants of time. Alternatively, Kirchhoffs voltage law can be stated in terms of voltage drops and rises as follows. The sum of voltage rises and drops in a closed loop at any instant of time are equal. KVL is a consequence of law of conservation of energy as voltage is energy or work per unit charge. If we start from one node in a loop and move along the closed loop and comeback to the same node, obviously the total potential difference or sum of potential rises must equal the total sum of potential falls. Just as, if we start from one point on the surface of the earth and after travelling through valleys and hills come back to the same point, the total displacement is zero. We talk elevation's and depression on the earth with respect to the sea level. Similarly, in case of voltages we take ground as the reference which is shown in Fig. i. 7(a). Here potential of node A is above the ground and that of B is below the ground potential.

We know that electronic current flows from negative potential to positive potential, the conventional current flows from positive potential to negative potential. Therefore, when current i flows in the circuit of Fig. i.7 (b) it produces voltages polarites in various elements as shown in the figure. Applying Kirchhoffs voltage law

V1 + V2 + U3 - V = 0

 Or in terms of voltage drops and voltage rises

u 1 + u2 + u3 = V
Kirchhoffs current law states that the algebraic sum of all currents terminating at a node equals zero at any instant of time. Alternatively, this states that sum of all currents entering a node equals the sum of currents leaving the same node at any instant of time.

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