Introduction:
In this question, we have two resistors of 2 ohm and 3 ohm connected in parallel. We need to calculate the ratio of electric power consumed by both resistors.

Explanation:
When resistors are connected in parallel, the voltage across each resistor is the same. However, the current passing through each resistor is different. The formula for calculating the total resistance in parallel is:

1/R(total) = 1/R1 + 1/R2 + ...

Using this formula, we can find the total resistance of the circuit which is:

1/R(total) = 1/2 + 1/3
R(total) = 1.2ohms

Now, we can calculate the current passing through each resistor using Ohm's law:

I1 = V/R1 = V/2
I2 = V/R2 = V/3

Since the voltage across both resistors is the same, we can equate the two expressions for current:

V/2 = V/3
V = 6V/5

Now we can calculate the power consumed by each resistor using the formula:

P = VI

For the 2 ohm resistor:

P1 = (6V/5)(V/2) = 6V^2/10 = 0.6V^2

For the 3 ohm resistor:

P2 = (6V/5)(V/3) = 2V^2/5 = 0.4V^2

The ratio of the power consumed by the 2 ohm resistor to the 3 ohm resistor is:

P1/P2 = 0.6V^2/0.4V^2 = 3/2

Therefore, the ratio of electric power consumed by the 2 ohm resistor to the 3 ohm resistor is 3:2.

Conclusion:
In conclusion, we found that the ratio of electric power consumed by the 2 ohm resistor to the 3 ohm resistor is 3:2. This was calculated by first finding the total resistance of the circuit, then using Ohm's law to find the current passing through each resistor, and finally using the formula for power to calculate the power consumed by each resistor.

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