For the circuit shown in the figure below, use Kirchhoff\'s rules to obtain equa

Question

For the circuit shown in the figure below, use Kirchhoff's rules to obtain equations for the upper loop, the lower loop, and the node on the left side. In each case suppress units for clarity and simplify, combining like terms. (Use the following as necessary: I18, I12, and I36.)

(a) the upper loop

(b) the lower loop

(c) the node on the left side

(d) Solve the node equation for I36.

(e) Using the equation found in (d), eliminate I36 from the equation found in part (b).

(f) Solve the equations found in part (a) and part (e) simultaneously for the two unknowns for I12 and I18, respectively.

(g) Substitute the answers found in part (f) into the node equation found in part (d), solving for I36.
I36 = 8 A

(h) What is the significance of the negative answer for I12?

Explanation / Answer

1)

Using Kirchoff's Voltage law in Upper loop

- 18 + I18 (8) + I12 (11) - 12 + I12 (7) + I18 (5) = 0

13 I18 + 18 I12 = 30                   Eq-1

2)

Using Kirchoff's Voltage law in Upper loop

I12 (11) - 12 + I12 (7) + 36 - I36 (5) = 0

5 I36 - 18 I12 = 24                             Eq-2

3)

I36 + I12 = I18 Eq-3

4)

using eq-1 and eq-3

13 (I36 + I12 ) + 18 I12 = 30  

13 I36 + 31 I12 = 30    eq-4

5 I36 - 18 I12 = 24                             Eq-2

Using eq-2 and eq-4

I36 = 3.3

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