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The value of unknown resistance (x) for which the potential difference between B and D will be zero in the arrangement shown, is [Figure: bridge ABCD with a 14.5 V cell connected between A and C. Arm AB: 24 Ω in parallel with a series pair 12 Ω + 12 Ω. Arm BC: 1 Ω in parallel with 1 Ω. Arm AD: x Ω in series with a parallel pair of 12 Ω and 12 Ω. Arm DC: 0.5 Ω. Nothing is connected between B and D.]

Asked in JEE Main 6th April 1st Shift 2024 · Wheatstone bridge

Figure: Wheatstone bridge
Answer: (3) 6 Ω

Step-by-step solution

V_B=V_D means the bridge is balanced: (R_AB)/(R_BC)=(R_AD)/(R_DC).

R_AB=24∥(12+12)=12 Ω and R_BC=1∥1=0.5 Ω.

R_AD=x+(12∥12)=x+6 and R_DC=0.5 Ω.

(12)/(0.5)=(x+6)/(0.5) gives x+6=12.

x=6 Ω (the cell voltage does not matter).

Why the other options are wrong

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