Kirchhoff S Laws

Apply Kirchhoff’s Current Law (KCL) at the central node. Incoming currents: -

1%20%5C%2C%20%5Ctext%7BA%7D

(top-left) -

5%20%5C%2C%20%5Ctext%7BA%7D

(middle-left) -

1%20%5C%2C%20%5Ctext%7BA%7D

(bottom-left)

%5Ctext%7BTotal%20In%7D%20%3D%201%20%2B%205%20%2B%201%20%3D%207%20%5C%2C%20%5Ctext%7BA%7D

Outgoing currents: -

3%20%5C%2C%20%5Ctext%7BA%7D

(top-right) -

2%20%5C%2C%20%5Ctext%7BA%7D

(middle-right) -

3%20%5C%2C%20%5Ctext%7BA%7D

(bottom-right) -

I

(downward)

%5Ctext%7BTotal%20Out%7D%20%3D%203%20%2B%202%20%2B%203%20%2B%20I%20%3D%208%20%2B%20I

Applying KCL:

7%20%3D%208%20%2B%20I%20%5Cquad%20%5CRightarrow%20%5Cquad%20I%20%3D%20-1%20%5C%2C%20%5Ctext%7BA%7D

Since current comes out as negative, the actual direction of current is upward, and magnitude is:

%5Cboxed%7BI%20%3D%201%20%5C%2C%20%5Ctext%7BA%7D%20%5Ctext%7B%20upward%7D%7D

Now, consider the bottom vertical branch:

%5Ctext%7BIncoming%3A%20%7D%204%20%5C%2C%20%5Ctext%7BA%7D%2C%20%5Cquad%20%5Ctext%7BOutgoing%3A%20%7D%20I%20%2B%203%20%5C%2C%20%5Ctext%7BA%7D%0A%5CRightarrow%204%20%3D%20I%20%2B%203%20%5CRightarrow%20I%20%3D%201%20%5C%2C%20%5Ctext%7BA%7D

So the total downward current in the figure must be:

I%20%3D%20%5Cboxed%7B8%20%5C%2C%20%5Ctext%7BA%7D%7D

Chapter Questions
1 MCQs