Question

Use the node-voltage method to find how much power the current source extracts from the circuit(Figure 1) if i = 2.6A and v = 60V .

Thanks

Answer 1

let the bottom node of current source be at ground.

the node at intersection of 50 ohms and 1 ohms is v1.

let the node at intersection of 1 ohms and voltage source be at v2 volts.

then node at intersection of 4 ohms and voltage source v will be v2-60 volts

then using KCL at node connecting 50 ohms and 1 ohms:

i=v1/50 + (v1-v2)/1

50*i=v1+50*v1-50*v2

130=51*v1-50*v2...(1)

now using kcl at node v2:

(v1-v2)/1= (v2-60-0)/4

4*v1-4*v2=v2-60

4*v1=5*v2-60

v1=1.25*v2-15..(2)

putting expression for v1 in equation 1,

130=51*(1.25*v2-15)-50*v2

v2=65.091 volts

then v1=66.364 volts

so voltage across current source=66.364 volts

hence power provided by the current source=current *velocity=172.55 W