Page 84 - Matrix Analysis & Applied Linear Algebra

2.6 Electrical Circuits 77

2.6.4. Consider the circuit shown below and answer the following questions.

R 2 R 3

R 5

R 1 R 4
R 6

I E

(a) How many nodes does the circuit contain?
(b) How many branches does the circuit contain?
(c) Determine the total number of loops and then determine the
number of simple loops.
(d) Demonstrate that the simple loop equations form an “indepen-
dent” system of equations in the sense that there are no redun-
dant equations.
(e) Verify that any three of the nodal equations constitute an “in-
dependent” system of equations.
(f) Verify that the loop equation associated with the loop containing
R 1 ,R 2 ,R 3 , and R 4 can be expressed as the sum of the two
equations associated with the two simple loops contained in the
larger loop.
(g) Determine the indicated current I if R 1 = R 2 = R 3 = R 4 =1
ohm, R 5 = R 6 = 5 ohms, and E = 5 volts.