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Kirchoff's voltage law states that the algebraic sum of all branch voltages around any closed path in a circuit is always zero.
By using Kirchoff's Voltage law, the sum of the potential drops is equal to the sum of the potential rises.
30 V = 2V + 5V + 3V + ?V + 10V + 6V
?V = 4V.
Kirchhoff's current law states that the sum of the current entering into any node is equal to sum of the currents leaving that node.
By applying kirchhoff's current law,
I (entering current) = I 1 + I 2 + I 3 (leaving current)
I = V / 1 + V / 2 + V / 3
10A = V [ 1 / 1 + 1 / 2 + 1 / 3 ]
10A = V [ 1 + 0.5 + 0.333 ]
V = 10 A / 1.83
V = 5.46 V
Clearly, by using ohm's law I = V / R
I 1 = 5.46 / 1 = 5.46A
I 2 = 5.46 / 2 = 2.73A
I 3 = 5.46 / 3 = 1.82A
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