Linear circuit analysis question

[arkturus]

Homework Statement

Replace resistor R with a voltage source such that no power is absorbed by either resistor; draw the circuit, indicating the voltage polarity of the new source.

Homework Equations

Ohm's law, Power = IV = I^2 * R

The Attempt at a Solution

I'm honestly not too sure how to begin the problem. The total voltage across the circuit should add up to zero, so I'm guessing the new voltage source must be 12V, but that seems too simple.

Thanks for the help.

 

[skeptic2]

What must the voltage be across a resistor in order for that resistor not to dissipate power? What would the voltage of a voltage source at R be in order to achieve that condition?

E.g., start with the 15 k resistor at the top. What would the voltage have to be at the top of R in order for the 15k resistor not to dissipate power?

 

[arkturus]

What must the voltage be across a resistor in order for that resistor not to dissipate power? What would the voltage of a voltage source at R be in order to achieve that condition?

E.g., start with the 15 k resistor at the top. What would the voltage have to be at the top of R in order for the 15k resistor not to dissipate power?

I'm honestly not sure what the voltage must be through a resistor in order for it to not dissipate power. Is there a relationship I'm missing?

 

[skeptic2]

What is the formula for power dissipated by a resistor in terms of voltage?

 

[arkturus]

What is the formula for power dissipated by a resistor in terms of voltage?

Ah, got it. I was thinking in terms of P = I*V, but P = V^2/R works too.

I think my issue with the problem is the phrasing of "dissipating power". Does that mean that power will be zero?

I'm assuming the voltages would have to be 0 in order for power to be zero.

 

[skeptic2]

That's right, power is zero when the voltage is zero. What voltage would a voltage source at R have to be to get zero volts across the resistors?

 

[arkturus]

That's right, power is zero when the voltage is zero. What voltage would a voltage source at R have to be to get zero volts across the resistors?

Ah I got it, R should be replace with +12 volts. That way there is a net voltage of 0 throughout the circuit thus power at the top and bottom resistors must be 0?

 

[skeptic2]

Very good.

 

[arkturus]

Thanks a lot, you were a big help