# Power consumption in a Wheatstone bridge

Q1) Explain how the power consumption of each resistor will change as the resistance of Rs increases.

A) It is a circuit in which parallel connections of R1 and Rx and parallel connections of R2 and Rs are connected in series. Therefore, as the resistance of Rs increases, the combined resistance of R2 and Rs increases, and the voltage applied to R1 and Rx decreases, and the voltage applied to R2 and Rs increases. By the power consumption formula P = V2/R the power consumption of R1 and Rx decreases and the power consumption of R2 and Rs increases.

This is what I think about this question, but using simulation, the increase of voltage between Rs is not faster(?) than the increase of resistance of Rs, so Rs might increase or decrease. Is this right?

• Consider what happens to the circuit as Rs approaches infinity (open circuit).
– vir
Commented Sep 9, 2022 at 21:48
• @vir what do you mean Rs approaches infinity? the question is about how the power consumption of each resistor will change as the resistance of Rs increases. Commented Sep 9, 2022 at 22:36
• @moonjy1120 Vir is suggesting a technique often used in physics. If it's not obvious how something reacts to a small change, then take the change all the way, to zero or infiniity, as the result will often be easier to see intuitively. Now realise that a small change just changes things less than your extreme change, and you'll have the answer. Commented Sep 10, 2022 at 4:32

The current $$\ I\$$ through the Rs+Rx pair is E/(Rs+Rx) and power in each of the resistors is just $$\I^2\cdot R\$$
You will also find that there is a maxima in the power in Rs at Rs=Rx (where $$\ 0 = \frac{R_X^2 - R_S^2}{(R_S+R_X)^4}\$$ ) just as you would expect from the maximum power transfer theorem.