The current going through the resistor R 1 in the figure does not change whether

Question

The current going through the resistor R1 in the figure does not change whether the two switches S1and S2 are both open or both closed.
The resistances are R1 = 80.00 ?, R2 = 110.00 ?, and R3 = 52.00 ?. The voltage is V = 9.0 V.
With this information, what is the value of the unknown resistance R?

The current going through the resistor R1 in the figure does not change whether the two switches S1 and S2 are both open or both closed. The resistances are R1 = 80.00 ?, R2 = 110.00 ?, and R3 = 52.00 ?. The voltage is V = 9.0 V. With this information, what is the value of the unknown resistance R?

Explanation / Answer

if both are open,

eq resiattance =R1+R2+R3=242 ohm

I=9/242 A.

now if both are closed eq.resistance = R2+ R||R1

=110 +80R/80+R.

I=9/Req

I through R1= (9/Req )*(R/R+80)

=> 9/242= 9R/(110*80 + 190R)

=> R=2200/13=169.23 ohm

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