Final answer:
The power dissipated in R2 with resistance 2R can be found by using the power dissipation formula P = I²R and Ohm's law. Starting with the known power in R, the current I2 through R2 is half of I. This information allows calculation of the power dissipated in R2.
Step-by-step explanation:
To determine the current through resistor 2 (which we will call R2), we need to understand the power dissipation formula for a resistor, P = I²R. Given that the power dissipated in resistor 1 (R) is 10W, we can express the power dissipated in R2, which has a resistance of 2R, using a derived version of this formula. The relationship between the power dissipated in R and the power dissipated in R2 can be understood through the ratios of their resistances.
Starting with the power dissipation in R, which is marked as P = I²R = 10W, and knowing P2 (the power in 2R) can be expressed as P2 = (I2)²(2R), where I2 is the current through R2, we need to find the current I2. Since resistors R and 2R are connected to the same voltage source, the voltage across them must be the same. Thus, by Ohm's law (V = IR), we can deduce that the current through R2 will be half of the current through R because R2 is twice the resistance of R. Hence, we can state that (I2)² = (I/2)². Given that I can be derived from the initial power equation for R, we can calculate I and then find I2 which is the current through R2.
Once we have the value of I2, the power dissipated in R2, which is P2 = 2(I2)²R, can also be found. It is important to remember, to apply Ohm's law correctly, the total circuit conditions must be considered. We have outlined how to to use the given data and the power formula to find the required current and power values.