Final answer:
In a series circuit, the power dissipated across resistors is dependent on their resistance. Using the formula P = V^2 / R, we can find the voltage across each resistor in the circuit.
Step-by-step explanation:
In a series circuit, the total voltage across the resistors is shared between them based on their resistance. Since the resistors in question have resistance values of R and 2R, and the power dissipated in R is given as 10 W, we can use the formula P = V^2 / R to find the voltage across R.
Plugging in the given values, we have 10 W = V^2 / R. Since the power is equal to V^2 / R, we can rearrange the formula to solve for V: V = sqrt(P * R).
Substituting the given values, we find V = sqrt(10 W * R). The voltage across R is sqrt(10 R) volts. Similarly, the voltage across 2R would be sqrt(10 * 2R) volts.