What is the Resistance of Resistor X?

[Soaring Crane]

Homework Statement

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

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.

 

[Doc Al]

Looks good to me!

 

[m2003]

Your approach to solving the resistor network is correct. The 75.0 ohm and 55.0 ohm resistors are indeed in series, and the X resistor is in parallel with the equivalent resistance of the 115.0 ohm, 130.0 ohm, and 85.0 ohm resistors. Your calculation of the equivalent resistance is also accurate, resulting in a value of 46.8 ohms for the X resistor. This means that the X resistor has a resistance of 46.8 ohms, which is the value that the ohmmeter reads. Well done!