What is the Resistance of Resistor X?

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The discussion revolves around calculating the resistance of resistor X in a network where an ohmmeter reads 20.2 ohms. The user attempts to determine if the 75.0 ohm and 55.0 ohm resistors are in series, leading to a combined resistance of 115.0 ohms, which is then used in a parallel calculation with other resistors. The user applies the formula for equivalent resistance in parallel circuits but expresses uncertainty about their approach and whether they considered all necessary properties of ohmmeter readings. After calculations, they arrive at a resistance value of approximately 46.8 ohms for resistor X. Overall, the user seeks confirmation of their method and results.
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Homework Statement



For the resistor network shown in the figure, the ohmmeter reads 20.2 ohm.

yf_Figure_26_491.jpg


What is the resistance of the resistor X?


Homework Equations



See below.

The Attempt at a Solution



I’m uncertain if I tackled the system correctly, so please guide me on any misconceptions in my workings.

For an ohmmeter, I didn’t come across any special formulas like for a voltmeter, and I may have not addressed any typical properties for ohmmeter readings . . .

Are the 75.0 ohm and 55.0 ohm in series? And then X; R_75+55; R_115, and R_85 will be in parallel?

(1/R_eq) = (1/R_x) +(1/115.0 ohm) +(1/130.0 ohm) + (1/85 ohm)
(1/R_x) = (1/20.2 ohm) – (1/115.0 ohm) –(1/130 ohm) – (1/85 ohm)
= 0.02135 1/ohm

R_x = 1/0.0214 1/ohm = 46.8 ohm ?

Thanks.
 
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