Calculating Total Resistance:
To find the total resistance in the circuit, we can start by considering the resistance of each individual edge. Since all the resistors have the same value, we can calculate the equivalent resistance of two resistors in series and then combine them in parallel.

- Two resistors in series: When two resistors are connected in series, their resistances add up. Therefore, the resistance between two adjacent corners of the cube is 2 + 2 = 4 ohms.

- Combining resistors in parallel: When resistors are connected in parallel, their resistances can be calculated using the formula: 1/Req = 1/R1 + 1/R2 + 1/R3 + ...

Since there are twelve resistors, we can calculate the equivalent resistance of all of them combined in parallel:

1/Req = 1/4 + 1/4 + 1/4 + ... (12 times)

1/Req = 12/4 = 3/1

Req = 1/3 ohm

Calculating Total Voltage:
The battery is connected between two adjacent corners of the cube. This means that the potential difference across the battery is equal to the voltage of the battery.

Vbattery = 2 volts

Calculating Total Current:
To find the total current drawn from the battery, we can use Ohm's Law:

I = V/R

Where I is the current, V is the voltage, and R is the resistance.

Using the value of the equivalent resistance calculated earlier:

I = 2 volts / (1/3 ohm + 0.1 ohm)

I = 2 volts / (1.3 ohm)

I ≈ 1.538 ampere

Therefore, the current drawn from the battery is approximately 1.538 amperes.

Explanation and Conclusion:
When a 2-volt battery is connected between two adjacent corners of the cube, a current of approximately 1.538 amperes is drawn from the battery. This is because the equivalent resistance of the circuit is 1/3 ohm, which determines the flow of current according to Ohm's Law. The internal resistance of the battery (0.1 ohm) is also taken into account while calculating the current.