How to find power dissipation in combination circuit?

[boilerpilot]

Homework Statement

What is the power dissipated in the 34-Ohm resistor?

Homework Equations

P=RI^2

The Attempt at a Solution

I have found the total current in the system as well as the current through the resistor, and keep getting 1.88, which is incorrect. Any suggestions on where I am going wrong?

 

[ehild]

Nobody can find your mistake without seeing your work.

ehild

 

[boilerpilot]

Ok, I guess I need to clarify my work. Here is what I have so far...

R_total=35.88
I=8/35.88=.222965
P=E²/R
P=8²/34
P=1.8823W

The part that confuses me is the combination circuit part, and I am not sure how that plays into the power dissipation of the resistor...

 

[ehild]

The voltage is not 8 V across the 34 ohm resistor. Try to find it out.
The parallel resistors can be replaced by their resultant, and this is in series with the 25 ohm resistor. You know the current flowing both series resistors. What is the voltage across the resultant of the parallel ones?

ehild

 

[boilerpilot]

The voltage is not 8 V across the 34 ohm resistor. Try to find it out.
The parallel resistors can be replaced by their resultant, and this is in series with the 25 ohm resistor. You know the current flowing both series resistors. What is the voltage across the resultant of the parallel ones?

ehild

I don't really know what you mean. Isn't voltage equal across a parallel circuit? I also don't know what you mean by two series resistors...Is this circuit a series (with the 16 and 25 Ohm) with a parallel circuit (34 Ohm)? Or a parallel (16 and 34) with one in series (25 Ohm)? I have tried to solve this either way, but I can't figure out how much power is dissipated in that 34 Ohm resistor.

 

[berkeman]

I don't really know what you mean. Isn't voltage equal across a parallel circuit? I also don't know what you mean by two series resistors...Is this circuit a series (with the 16 and 25 Ohm) with a parallel circuit (34 Ohm)? Or a parallel (16 and 34) with one in series (25 Ohm)? I have tried to solve this either way, but I can't figure out how much power is dissipated in that 34 Ohm resistor.

I'd just combine all the resistors (I think you did this at one point), to find out what the current is through the circuit. All that current goes through the bottom resistor, so you can calculate the voltage across that resistor. The rest of the voltage is across the parallel combination of resistors to the left, and there's an equation for power dissipated in a resistor when it has a voltage across it...

 

[boilerpilot]

I'd just combine all the resistors (I think you did this at one point), to find out what the current is through the circuit. All that current goes through the bottom resistor, so you can calculate the voltage across that resistor. The rest of the voltage is across the parallel combination of resistors to the left, and there's an equation for power dissipated in a resistor when it has a voltage across it...

The current through the 25 Ohm resistor is .222965A. This means the voltage across the resistor is 5.574V. This leaves 2.426V unaccounted for. How do I know how much power is dissipated from the rightmost resistor?

 

[berkeman]

The current through the 25 Ohm resistor is .222965A. This means the voltage across the resistor is 5.574V. This leaves 2.426V unaccounted for. How do I know how much power is dissipated from the rightmost resistor?

That leftover voltage is across both of the right-hand resistors. What's the equation for the power dissipated in a resistor based on the voltage across it and the resistance? You can use that same formula to calculate the power dissipated across each of the right side resistors individually.

 

[boilerpilot]

That leftover voltage is across both of the right-hand resistors. What's the equation for the power dissipated in a resistor based on the voltage across it and the resistance? You can use that same formula to calculate the power dissipated across each of the right side resistors individually.

P=RI²=V²/R

Assuming this is the correct equation, I know R (34 Ohms) but that's it, right? I don't know current or voltage (the only voltage I know is what's left over). How can I separate that to find what I need for the 34 Ohm resistor?

 

[ehild]

I don't really know what you mean. Isn't voltage equal across a parallel circuit? I also don't know what you mean by two series resistors...Is this circuit a series (with the 16 and 25 Ohm) with a parallel circuit (34 Ohm)? Or a parallel (16 and 34) with one in series (25 Ohm)? I have tried to solve this either way, but I can't figure out how much power is dissipated in that 34 Ohm resistor.

The voltage is equal across parallel connected resistors. How do you know if two resistors are connected in parallel? Which ones in this circuit are connected in parallel?

ehild

 

[boilerpilot]

The voltage is equal across parallel connected resistors. How do you know if two resistors are connected in parallel? Which ones in this circuit are connected in parallel?

ehild

It looks to me like the 16 Ohm and 34 Ohm resistors are in parallel. Is that correct? Does this mean that the 16 Ohm and 34 Ohm resistors each have 2.426V across them?

 

[berkeman]

It looks to me like the 16 Ohm and 34 Ohm resistors are in parallel. Is that correct? Does this mean that the 16 Ohm and 34 Ohm resistors each have 2.426V across them?

Yes.

 

[boilerpilot]

Yes.

So...for the win...

P=V²/R
P=2.426²/34
P=.1731W

Is this correct?

 

[ehild]

Yes.

ehild

 

[boilerpilot]

Yes.

ehild

Thanks ehild and berkeman for all the help. I sincerely appreciate it.