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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 ​​ ​​ ?

Respuesta :

Answer:4

Explanation:

For same Power one device is operated at [tex]V_1=120 V[/tex] and another at [tex]V_2=240\ V[/tex]

Suppose [tex]R_1[/tex] and [tex]R_2[/tex] is the resistance of first and second device respectively

using [tex]P=\frac{V^}{R}[/tex]

For first device

[tex]P=\frac{(120)^2}{R_1}[/tex]

[tex]R_1=\frac{120^2}{P} [/tex]

For second Device

[tex]R_2=\frac{240^}{P}[/tex]

Ratio of resistances are

[tex]\frac{R_2}{R_1}=\frac{240^2}{120^2}[/tex]

[tex]\frac{R_2}{R_1}=(2)^2[/tex]

[tex]\frac{R_2}{R_1}=4[/tex]

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