# Electric Circuits: Loop Analysis

Please see attached problem and solve all parts using Loop Analysis only.

Find all the currents in the circuit. Indicate all the voltage polarities and current directions.

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#### Solution Preview

For convenience the nodes have been numbered 1,2,3... There are four independent loops. Let the loop currents be I3, I4, I5 and I6 as shown. We can now write the loop equations using Kirchhoff's voltage law as follows:

For loop 1: R3 (I3 - I5) + V42 + R1 I3 = 0

Substituting values: 10000 (I3 - I5) + V42 + 10000 I3 = 0 ...(1)

For loop 2: R4 (I4 - I6) + R2 I4 + V24 = 0

Substituting values: 10000 (I4 - I6) + 10000 I4 + V24 = 0 ...(2)

Adding (1) and (2): 10000 (I3 - I5) + V42 + 10000 I3 +10000 (I4 - I6) + 10000 I4 + V24 = 0

=> 20000 I3 + 20000 I4 - 10000 I5 - 10000 I6 = 0 (as V42 = - V24) ...(3)

For loop 3: R6 I5 + R5 (I5 - I6) + R3 (I5 - I3) + V1 = 0

Substituting values: 10000 I5 + 10000 (I5 - I6) + 10000 (I5 - I3) + 5 = ...

#### Solution Summary

The expert examines a loop analysis on an electric circuit.