A uniform metallic wire of total resistance 4 Ω is bent into a square loop ABCD. A 2 Ω resistor is connected between B and D, and a 2 V battery is connected across opposite vertices A and C (see figure). Find the battery current I. Image
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Question

A uniform metallic wire of total resistance 4 Ω is bent into a square loop ABCD. A 2 Ω resistor is connected between B and D, and a 2 V battery is connected across opposite vertices A and C (see figure). Find the battery current I. Image

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G1 Physics · Accepted Answer

Step 1: Since four sides are equal, the resistance of each side is 4/4 = 1 Ω. Step 2: The square is symmetrical about the line AC. Therefore the potentials of B and D are equal; no current flows through the 2 Ω resistor connecting B and D (balanced bridge). Step 3: The path A–B–C has resistance 1 + 1 = 2 Ω. The path A–D–C also has resistance 1 + 1 = 2 Ω. These paths are in parallel. Step 4: R(equivalent) = (2 × 2)/(2 + 2) = 1 Ω. Step 5: I = V/R(equivalent) = 2/1 = 2 A. Final answer: 2 A (Option…