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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?

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  • \$\begingroup\$ Consider what happens to the circuit as Rs approaches infinity (open circuit). \$\endgroup\$
    – vir
    Commented Sep 9, 2022 at 21:48
  • \$\begingroup\$ @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. \$\endgroup\$
    – moonjy1120
    Commented Sep 9, 2022 at 22:36
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    \$\begingroup\$ @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. \$\endgroup\$
    – Neil_UK
    Commented Sep 10, 2022 at 4:32

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If the current through 'G' can be ignored (as implied by the annotations), the answer is very easy.

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\$

If you differentiate power in each resistor wrt Rs you can see that power in Rx increases monotonically with decreasing Rs >= 0.

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.

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  • \$\begingroup\$ Thank you for answer! I got some question about this... From what I understand, as the resistance of Rs increases the current through 'G' occurs so we have to consider that current too (the annotation is implying currently there is no current through 'G' and question is about what if Rs increases) \$\endgroup\$
    – moonjy1120
    Commented Sep 11, 2022 at 2:28
  • \$\begingroup\$ As the resistance of Rs change from bridge balance (either up or down) then current could flow through G if it has significant conductance. We actually don't know if the bridge is balanced or not to start with since no values are given. Obviously if the power in Rx increases monotonically with decreasing Rs, then it must decrease monotonically with increasing Rs resistance, right? \$\endgroup\$ Commented Sep 11, 2022 at 8:39

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