# Power delivered by this dependent voltage source How can I approach this type of problem? Which different methods can be used here? KVL, supernode, mesh-analysis, source transform.

I tried using KCL on a node assuming its voltage V1:

2=(V1-10)/1 + (V1-4Vo)/4
Solving we get eqn :
5V1-4Vo=48  ...(1)


How can I form the second equation?

Assuming loop currents i1 and i2 (clockwise),
so i1=-2
Vo=(i2+2)*1 ..(total current is i2+2 isn't it?)
second loop eqn is:
-10-Vo+4i2+4Vo=0
3Vo+4i2=10
3(i2+2)+4i2=10
3i2+6+4i2=10
i2=4/7 Amp (Probably wrong! Why?)
Vo=(4/7)+2= 2.57
4Vo=10.28
Power=(10.28)^2 * (4/7)=Wrong
the 4 answer options are +/- 1152 or +/- 1200


• The correct answer is 1152 watts BTW. 16 amps flows through the 4 ohm resistor. Apr 9 at 13:08
• P=I^2*R so 16*16*4= 1024 .How you got 1152? can you elaborate the mistake in my approach
Apr 9 at 13:10
• I just simulated it for convenience. Modern sims give very exact results. If you simulate you can begin to see the relationships and double check your math. Apr 9 at 13:11
• Without simulations what to do to find i in right loop still can't find mistakes, is Vo=-2 if so then 4Vo is -8 and to get 1152 Watts i have to have 144 amps current in second loop which seems too large?
Apr 9 at 13:36

How to approach this type of problem? (KVL, supernode, mesh-analysis, source transform)?

These are my KVL equations: - So, from the first equation: -

$$3\cdot V_0 = 18 - 4\cdot I_1$$

Substitute the 2nd equation into the first equation: -

$$3\cdot (-I_1) = 18 - 4\cdot I_1$$

Hence $$\\hspace{1cm}I_1 = 18 \$$ amps $$\\hspace{1cm}\$$and,$$\\hspace{1cm}\$$ $$\V_0 = -18\$$ volts  This of course means that the voltage magnitude across the dependent source is 72 volts and, the current flowing into it is 16 amps. This makes it dissipate 1152 watts.

Your (V1-10) happens also be =Vo. Use it in the rightmost branch current in the KCL equation.

• 5(Vo +10)-4Vo=48 which means Vo=-2 putting that in KCL loop -10+i+2+4i+4(-2)=0 ; i =16/5 and power=Vxi , 8 * 16/5 == 25.6, but the answer is either +/- 1152 or +/- 1200 Watts. What is the mistake here ?