Node Voltage Method roblem 4.29 Assume you are a project angineer and one of you

Question

Node Voltage Method roblem 4.29 Assume you are a project angineer and one of your staff is assigned to analyze the circuit shown in (Figure 1). Suppose that R= 2 k The reference node and node numbers given on the figure were assigned by the analyst. Her solution gives the values o and v as 150 V and 100 V, respectively Part A What value did the analyst use for the left-most node voltage when writing KCL equations at nodes 1 and 2? Express your answer in terms of i, Submit t Answe Part B What valus did the analyst use for the right-most node voltage when writing KCL equations at nodes 1 and 2? Express your answer in terms of i UR = Submit gure 1 af 1 Part C 12%, Use the vakues supplied by the analyst to calculate the magnitudes of the total power developed in the circuit arnd the tatal power dissipated in the circui Express your answers using three significant figures separated by a comma. 12x10 25 kn SV Submit

Explanation / Answer

Part A )

left side VL = 75 - 1250 i

Part B )

right side is VR = 75 V

Part C )

i = V1 - V2 / 500

i = 150 - 100 / 500

i = 0.1 A

V = V2 - 75 = 100 - 75

V ' = 25 V

VL = 75 - 1250 X 0.1

= - 50 V

ix = ( VL - V1 ) / 1000 + VL / 2500

ix = - 0.22 A

iy = V2 - 75 / 500 + 0.22

iy = 0.27 A

dissipation at top Ptop = 1250 i X ix

= - 27.5 W

dissipation at bottom

Pbottom = - V1 X 12 X 10-3 X V '

= - 45 W

P75 = 75 iy

= 75 X 0.27 = 20.25 W

P1k = ( VL -V1 )2 / 1000

= 40 W

P2.5 K = VL2 / 2500

= 5 W

P500 right = V ' 2 / 500

= 1.25 W

P2K = V22 / 2000

= 5 W

Pdissipated = - 27.5 - 45

= - 72.5 W

Pdissipated = 20.25 + 40 + 1 + 5 + 1.25 + 5

Pdissipated = 72.5 W

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