Loop Analysis Quiz (KVL), Quizzes of Electrical Circuit Analysis

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Chapter 3: Part 2

Michael Faraday (1791 to 1867)

“…value of Faraday's work today must be higher than the capitalization of all the shares on the Stock Exchange!”

Baroness Margaret Thatcher in a speech to the Royal Society in 1988

What is a branch

 A branch is a circuit element and its two nodes

i

We can use loop analysis to directly determine the current through it

What is a loop?

 A non-self intersecting closed path around a circuit.

See first lecture for details.

KCL reduces the number of

unknowns

i 1 i 1 + i 3^ i 3

i 4 i 6

i 1 - i 4 i 6 - i 3

i 4 + i 6

Combining Loop Currents

 - i i 

• i
• i 4 i 5 i
  • i
  • i 8 i
    • i i Identifying Branch Currents
• i
• i 4 i 5 i
  • i
  • i 8 i
• i 1 i
  • i 1 i
    • i 1 + i - i 6 - i
      • i

In General

 The minimum number of variables that are needed to

describe the branch currents is:

=B-N+

i i^1 + i^3^ i^3

1

i 4 i^6

i 1 - i 4 i 6 - i 3

i 4 + i 6

B=number of branches N=number of nodes

The Best!: Mesh Analysis

i 1 i 2

i 3 i 4

• No loop encompasses another
• All currents flow with the same sense (clockwise or counter clockwise)
• Always give the right number of loops

Loop currents are a figment of our

imagination; a mathematical construct

i 1 i 2

i 3 i 4

i 2 = 2 mA

i 4 − i 3 = 4 mA

Loop currents passing through Independent

Current Sources have fixed relationships

Practice using loop analysis