Question

Two different electrical devices have the same power consumption, but one is meant to be operated on 120-V AC and the other on 240-V AC. (a) What is the ratio of their resistances? (b) What is the ratio of their currents? (c) Assuming its resistance is unaffected, by what factor will the power increase if a 120-V AC device is connected to 240-V AC?

a) 1:4, 1:2, 4
b) 1:2, 1:1, 2
c) 1:2, 2:1, 4
d) 1:4, 2:1, 4

Answer 1

The resistance ratio of the two devices operating at different voltages is 1:4, the current ratio is 1:2, and if a 120-V AC device is connected to 240-V AC, the power increases by a factor of 4.

Step-by-step explanation:

Understanding the Electric Properties of Devices

Two different electrical devices have the same power consumption but are meant to be operated at different voltages (120-V AC and 240-V AC). As such:

• (a) The ratio of their resistances is determined by the formula for power (P = V^2/R), thus the device designed for 240-V AC must have a resistance four times greater than the one designed for 120-V AC, giving a resistance ratio of 1:4.
• (b) The ratio of their currents can be found using P = VI, so if two devices consume the same power, the device operating at a higher voltage draws less current. The current ratio is 1:2, with the device operating at the higher voltage drawing half the current.
• (c) If a device designed for 120-V AC is connected to 240-V AC its power consumption will increase by a factor of four, assuming the resistance remains unchanged. This is because power varies with the square of the voltage (P ≈ V^2/R), so doubling the voltage will quadruple the power, indicating a factor of 4.