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#
Authors:
J. David Irwin, R. Mark Nelms
Chapter:
Additional Analysis Techniques
Exercise:
Problems
Question:5 | ISBN:9780470633229 | Edition: 10

Question

Find V0 in the network in Fig. P5.5 using linearity and the assumption that V0=1V.

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Answer

0 0

Discussions

alvaro rodelo

from left to right:

Vs=8V, R1=3K,R2=3k,R3=3k,R4=3k in parallel with R4=3k,R5=6k, and R6=R7=3k

Assuming V0=1 = VR7 Then: IR6=IR7=1/3mA since they are on series, same current, VR7=1/3mA*3k = 1V and V36+VR7=2V

thefore: VR5 = VR4= 2V ,  so iR5=2v / 6K=1/3mA and IR4=2V/3k = 2/3mA

according to klc IR3 = iR4 + iR5 + IR6/7 = 4/3 mA, then VR3 = 3K * 4/3mA = 4V

and according to klv  VR2 = VR3 + VR4 = 6V, then IR2 = 6V / 3k = 2mA by ohm law

and klc on first node  IR1 = IR2 + IR3 = 2mA + 4/3mA = 10/3 mA

so by ohm: VR1= 10/3mA *3k = 10V,  so then Vs= VR1 + VR2 = 10V + 6V = 16V

but   since real Vs= 8V

then V0 = 8 / 16 = 1/2 = 0.5V,

i verified it with sumulator.

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