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JEE Main 2021 (27 Aug, Shift 2) · Combination of Resistors

Combination of Resistors question from JEE Main 2021 (27 Aug, Shift 2)

Q57JEE Main 2021 · 27 AUG · SHIFT 2Medium

Combination of Resistors

The ratio of the equivalent resistance of the network (shown in figure) between the points a and b when switch is open and switch is closed is x: 8. The value of x is ___________.

Figure

Numerical answer type. Work it out, then open the answer.

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Answer: 9

  1. Switch open: two paths each R+2R=3RR + 2R = 3R in parallel: Ropen=1.5RR_{open} = 1.5R.
  2. Switch closed: (R∥2R)+(2R∥R)=2R3+2R3=4R3(R \parallel 2R) + (2R \parallel R) = \dfrac{2R}{3} + \dfrac{2R}{3} = \dfrac{4R}{3}
  3. RopenRclosed=1.5R4R/3=98\dfrac{R_{open}}{R_{closed}} = \dfrac{1.5R}{4R/3} = \dfrac{9}{8}, so x=9x = 9.
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