Question

wo different electrical devices have the same power consumption, but one (device 1) is meant to be operated on 127 V AC and the other (device 2) on 230 V AC. (a) What is the ratio of their resistances? R2 R1 = (b) What is the ratio of their currents? I2 I1 = (c) Assuming its resistance is unaffected, by what factor will the power increase if a 127 V AC device (device 1) is connected to 230 V AC?

Answer 1

a) R₂/R₁ = 0.3049

b) I₂ / I₁ = 1.81

c) (230)² / ( 127)² = 3.28

Step-by-step explanation:

By definition the power consumption is:

P = I²*R ⇒ as I = V/R I² = (V/R)² and P = (V²/R²)*R

P = V²/R

P = power consumtion

I = current

R = is the resistor

Case Device 1 Voltage 127 (V)

P₁ = V₁² /R₁ P₁ = (127)²/ R₁

Case Device 2 Voltage 230 (V)

P₂ = ( 230)²/ R₂

As P₁ = P₂ (127)²/R₁ = (230)²/R₂

(127)²/(230)² = R₂/R₁

a) R₂/R₁ = 0.3049

b) P₁ = I₁²*R₁ P₂ = I₂²*R₂

I₂² *R₂ = I₁²*R₁

I₂² / I₁² = R₁/R₂

I₂² / I₁² = 1/ 0.3049

I₂² / I₁² = 3.2797

√ (I₂² / I₁² ) = √3.2797

b) I₂ / I₁ = 1.81

c) P₁ = V₁*I₁ ⇒ P₁ = V₁²/R₁ if we "use" the device in 230 (V)

P₁´ = V₂² / R₁

P₁ = (127)²/R₁ and P₁´ = (230)²/ R₁

Then the increasing factor is:

c) (230)² / ( 127)² = 3.28