Kirchhoffs Law - Using Kirchhoff’s Current Law and Ohm’s Law, find the magnitude and polarity

Kirchhoffs Law - Using Kirchhoff’s Current Law and Ohm’s Law find the magnitude and polarity

Question : Using Kirchhoff’s Current Law and Ohm’s Law, find the magnitude and polarity of voltage V in Figure given below. Directions of the two current sources are as shown.

Solution :

Let us arbitrarily choose the directions of I₁, I₂ and I₃ and polarity of V as shown in Figure given below. We will use the sign convention for currents as given in Article Determination of Voltage Sign. Applying applying Kirchhoff’s Current laws to node A, we have

− I₁ + 30 + I₂ − I₃ − 8 = 0

or I₁ − I₂ + I₃ = 22 ……………..(i)

Applying Ohm’s law to the three resistive branches in Figure given above, we have

(Please note the − ve sign.)

Substituting these values in (i) above, we get

OR V = 24V

∴ I₁ = V/2 = 24/2 = 12 A,

I₂ = − 24/6 = − 4 A,

I₃ = 24/4 = 6 A

The negative sign of I₂ indicates that actual direction of its flow is opposite to that shown in Figure given above. Actually, I₂, flows from A to B and not from B to A.

Read article – Units of Resistivity

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