Need help with a potential difference/resistance/current problem

[iiiiaann]

Homework Statement

The figure below shows a section of a circuit. The electric potential difference between points A and B that connect the section to the rest of the circuit is VA - VB = 87 V, and the current through the 6.0 resistor is i = 5.0 A.

(a) Is the device represented by "Box" absorbing or providing energy to the circuit?

(b) At what rate?

Homework Equations

iR=V

The Attempt at a Solution

So i know that the Box is providing energy, since the total potential around the loop has to be zero, and the current is traveling counter-clockwise, and the resistors cause the potential to go down, so the box must make the potential go back up, meaning it is adding energy. The hint i was given was:

How do you relate potential difference, current, and resistance? Can you find the potential across R1 and the box? If the box holds a battery, what is the orientation of its terminals?

I know the equation for current, resistance, and potential (iR=v) and i know that the terminals on the battery would be +- from left to right but I don't know how to go about calculating the rate

 

[gneill]

Since there's a potential from A to B, it may be that the net currents through the 6 and 4 Ohm resistors both flow to the right (and not in a "loop" as you suggest).

Take a look at the 6.0 Ohms resistor. You are given the current that flows through it. Does that suggest anything to you about the potential across it? (Hint: Ohm's Law).

What then must the potential across the 2.0 Ohm resistor be if the total from A to B is 87V? What's the current in that resistor?

 

[iiiiaann]

So the potential through the 6 ohm resistor is -30 V. So would that make the potential across the 2 Ohm resistor -57? That would mean the current through that resistor is 28.5. So the current through the 4 ohm resistor is 23.5 and therefore its potential is -94 V?

Is this right? if so where do i go from here?

 

[gneill]

So the potential through the 6 ohm resistor is -30 V. So would that make the potential across the 2 Ohm resistor -57? That would mean the current through that resistor is 28.5. So the current through the 4 ohm resistor is 23.5 and therefore its potential is -94 V?

Is this right? if so where do i go from here?

You're doing good!

If the potential drop across the 2.0 Ohm resistor is 57V, and the drop across the 4.0 Ohm resistor is 94V, the total drop along that path is 151V! That's larger than the 87V across A-B. So what does the box have to do to make the total drop come out to 87V? (Alternatively, the potential difference across the 4 Ohm resistor and the box should equal that across the 6.0 Ohm resistor: 30V)

 

[iiiiaann]

The box would have to boost the potential up by 64 V. So then the power of the batter is the voltage x the current though it. The voltage would be 64 and the current would be 23.5 so the power is 1504 W

Thanks for the help gettin my brain moving

 

[gneill]

The box would have to boost the potential up by 64 V, what next?

Well, what sort of component gives a voltage boost? Pencil the component into the schematic. Indicate the direction of current flow and any relevant polarities. What power is consumed or produced by that component? (How do you calculate it?)