Question

A wire of resistance 0.2 \( \Omega/{cm} \) is bent to form a square ABCD of side 10 cm. A similar wire is connected between the corners B and D. If 2 V battery is connected across A and C, the power dissipated is 

• A. 4 W
• B. 1 W
• C. 2 W
• D. 8 W

Hint:

When solving for power dissipated in a resistor, use \( P = \frac{V^2}{R} \), where \( V \) is the voltage across the resistor and \( R \) is the resistance.

Answer 1

The Correct Option is C

First, calculate the total resistance of the square: - The side length of the square is 10 cm, so the total resistance of the square formed by the wire is: \[ R_{{square}} = 0.2 \, \Omega/{cm} \times 10 \, {cm} = 2 \, \Omega \] Now, consider the wire connected between B and D. The total resistance in the path from A to C is calculated by combining the resistances in series and parallel. Using Ohm's law: \[ P = \frac{V^2}{R} \] Substituting the values: \[ P = \frac{2^2}{2} = 2 \, {W} \] Thus, the power dissipated is 2 W. 
Final Answer: 2 W.