In the diagram above, the ratio of he electric power dissipated in the 6Ω and the 3Ω resistor respectively is

Answer Details

To solve the problem, we can use the formula for electric power, which is P = VI, where P is power, V is voltage, and I is current. Using Ohm's law, we can also write V = IR, where R is resistance.
First, we need to find the current flowing through the circuit. Since the resistors are in parallel, the voltage across them is the same, and we can use Ohm's law to find the current through each resistor.
For the 6Ω resistor, V = IR = (12V)/(6Ω) = 2A
For the 3Ω resistor, V = IR = (12V)/(3Ω) = 4A
Now, we can calculate the power dissipated in each resistor using the formula P = VI.
For the 6Ω resistor, P = VI = (2A)(12V) = 24W
For the 3Ω resistor, P = VI = (4A)(12V) = 48W
The ratio of the power dissipated in the 6Ω resistor to that in the 3Ω resistor is 24W:48W, which simplifies to 1:2. Therefore, the answer is option (D) 1:2.