How to find the total power developed in the circuit and find the total power dissipated in the circuit?
First you need the voltage across and the current through every component/device, right? You might try mesh currents, but with that dependent current source you might rather go with node voltages- that's what I did. I called the top of the 3-ohm resistor "Vx" and the right side of the 1-ohm resistor "Vy". Then it's a pretty straightforward matter to obtain two equations in two unknowns. How do you handle V ∆ ? It's something minus something, right? In fact it's Vx - 125. Are you okay with KCL (Kircchoff's current law)? The sum of the currents COMING OUT of a node is zero... I'll get you started. The current moving from Vx toward 125 volts is (Vx - 125)/2. Once you get all your currents and voltage drops, how do you determine powers? VI, of course, but when is power being "given" ("developed", as you say)and "taken" ("dissipated")? When current flows from more positive to less positive (as in a resistor) it is being consumed by the resistor (i.e., dissipated by the resistor). That should be enough info to get you going...