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. What is the ratio of the resistance of 240V device to the resistance of the 120V device i.e. \frac{R_{240}}{R_{120}} ​R ​120 ​​ ​ ​R ​240 ​​ ​​ ?

Answer 1

Answer:4

Explanation:

For same Power one device is operated at $V_1=120 V$ and another at $V_2=240\ V$

Suppose $R_1$ and $R_2$ is the resistance of first and second device respectively

using $P=\frac{V^}{R}$

For first device

$P=\frac{(120)^2}{R_1}$

$R_1=\frac{120^2}{P}$

For second Device

$R_2=\frac{240^}{P}$

Ratio of resistances are

$\frac{R_2}{R_1}=\frac{240^2}{120^2}$

$\frac{R_2}{R_1}=(2)^2$

$\frac{R_2}{R_1}=4$