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NEETPhysicsCurrent Electricity

Five identical resistors, each of resistance R , are connected to form a square ABCD with a diagonal resistor connected between B and D. Match the connection cases in List I with their corresponding equivalent resistances in List II. List I List II (A) Equivalent resistance across AC (I) 5R 8 (B) Equivalent resistance across AB (II) 3R 4 (C) Equivalent resistance across BD (III) R (D) Equivalent resistance across AB

Options

  1. A(A)-(III), (B)-(II), (C)-(IV), (D)-(I)
  2. B(A)-(IV), (B)-(I), (C)-(III), (D)-(II)
  3. C(A)-(III), (B)-(I), (C)-(IV), (D)-(II)
  4. D(A)-(I), (B)-(III), (C)-(II), (D)-(IV)

Correct answer

C. (A)-(III), (B)-(I), (C)-(IV), (D)-(II)

Step-by-step solution

(A) Across AC: The circuit forms a balanced Wheatstone bridge. The diagonal BD acts as the galvanometer arm. Since the arms have equal resistance R , the bridge is balanced and no current flows through BD. The equivalent resistance is (R+R) (R+R) = 2R 2R = R . Thus, (A) matches (III). (B) Across AB: The resistor AB is in parallel with the rest of the network. The rest of the network consists of AD ( R ) in series with the parallel combination of DB ( R ) and DCB ( 2R ). The resistance of DB and DCB in parallel is R

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