Use the node-voltage method to find vo and the power delivered by the current source in the circuit in figure, if the v = 30V and the i = 1.9A . Use the node a as the reference node to find vo. Use the node b as the reference node to find vo. Find the power delivered by the 1.9A current source.

Answers

Answer 1

p=61.75W

(a)
use node a as reference and is shown in Figure 1

Apply KCL at super node  between b and c
=1.9+V^b/50+v^c/150+V^C?20+55=0
=v ^b/50+v^c/150+V^C/75=-1.9
=v^ b + v^ c=-1.9(50)
=v^ b +V^ C=-95.....(1)

From super node b and c,
v^ b-v ^c=30.....(2)

by solving equation 1 and 2
V^ b=-32.5V
V^ c=-62.5V

therefore the voltage V^ 0=-32.5V

(B) Apply KCL at node a.
-1.9+v^ a/50+v^ a- v^ c/150+v^a-v^c+20+55+0
V^ a/50+v^a-V^c/150+v^a-v^c/75=1.9
v^ a/50+v^a-v^c/50=1.9
v^ a+ v^ a - v^ c=1.9(50)
2V^ a -v^ c=95....(1)

put V^ c=-30v in equation(1)
2V^ a-(-30)=95
2V^ a=(95-30)
v^ a= 32.5V

From figure 2, the voltage v^ 0=-v^ a
therefore v^ 0=-32.5 V

(c)  power delivered by the 1.9 A current source is
p=iv^ 0
=(1.9)(-32.5)
=-61.75W
The negative sign indicates the power delivering by a source,

P=61.75W  

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Answer:

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The elastic modulus for steel given in the table is 207 GPa, which is in reasonable agreement with this value E = 200.75 GPa

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б2 = б1 / Э2 - Э1

Since stress-strain curves for all of the metals/alloys pass through the o

rigin, and if we take σ1 = 0 then ε1 = 0. Determinations of σ2 and ε2 are possible by moving the cursor to some arbitrary point in the linear region of the curve and then reading corresponding values in the “Stress” and “Strain” windows that are located below the plot.

(a) A screenshot for the titanium alloy in the elastic region is shown below

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| 492.4-0

0.0049-0

E=100489.79 MPA

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The elastic modulus for titanium given in the table is 107 GPA, which is in reasonably good agreement with this value.

(b) A screenshot for the tempered steel alloy in the elastic region is shown below

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E = 203711.11 MPA

E = 203.7 GPA

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(c) A screenshot for the aluminum alloy in the elastic region is shown below.

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193.6 – 0

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E = 69142.85 MPa

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(d) A screenshot for the carbon steel alloy in the elastic region is shown below

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160.6 – 0

0.0008 - 0

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