A wire whose resistance 0.1/cm is bent in the form of a square ABCD of side 10 cm. An exactly similar wire is connect across the points B and D. What will be the equivalent resistance between the other two corners A and C of the square?If a 2V battery be connected between A and C,then what will be the current drawn from the battery? If an ammeter be connected B and D,what will it read?

Question

Answer

**Equivalent Resistance between A and C:**

To find the equivalent resistance between points A and C, we can use the concept of resistors in parallel and series.

1. **Resistors in parallel:** The wires connected between points B and D are in parallel with the wire between points A and C. Since the wires are exactly similar, they have the same resistance of 0.1 Ω/cm.

2. **Resistors in series:** The wire between points B and D is in series with the wire between points A and C. The total length of the wire for both sections is 20 cm (10 cm for each section).

3. **Finding the equivalent resistance:** To find the equivalent resistance, we need to calculate the resistance of each section separately and then combine them.

a. Resistance of the wire between B and D: Since the total length of the wire is 10 cm, the resistance is given by R = ρ * (L/A) = 0.1 Ω/cm * (10 cm / 1 cm^2) = 1 Ω.

b. Resistance of the wire between A and C: Again, the total length of the wire is 10 cm, so the resistance is also 1 Ω.

c. Combining the resistances: The resistors are in series, so we add them up. The equivalent resistance is R_eq = R1 + R2 = 1 Ω + 1 Ω = 2 Ω.

**Current Drawn from the Battery:**

To find the current drawn from the battery, we can use Ohm's Law, which states that the current (I) flowing through a conductor is equal to the voltage (V) across the conductor divided by its resistance (R).

1. **Applying Ohm's Law:** We have a 2V battery connected between points A and C, and the equivalent resistance between these points is 2 Ω. Therefore, the current drawn from the battery is given by I = V / R = 2V / 2 Ω = 1A.

**Ammeter Reading between B and D:**

The ammeter connected between points B and D will measure the current flowing through that section of the wire.

1. **Calculating the current:** Since the wire between B and D has a resistance of 1 Ω, and there is a 2V potential difference across it (due to the battery), we can again use Ohm's Law to calculate the current. I = V / R = 2V / 1 Ω = 2A.

2. **Ammeter reading:** Therefore, the ammeter connected between B and D will read a current of 2A.

In summary, the equivalent resistance between points A and C is 2 Ω, the current drawn from the battery connected between A and C is 1A, and the ammeter connected between B and D will read a current of 2A.

Answer

0.5amp

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