Question

What is the ratio P1/P2P1/P2 of their power dissipations if the same current passes through each resistor

Answer 1

This question is incomplete, the complete question is;

Resistors 1 and 2 are connected to identical batteries, resistor 1 dissipates 4.0 times more power than resistor 2

What is the ratio P1/P2of their power dissipations if the same current passes through each resistor

Answer:

the ratio P₁/P₂ of their power dissipations is 0.25

Step-by-step explanation:

Given the data in the question;

`P_(i)` =
`I^(2) . R_i` --------------let this be equation 1

`P_(i)` =
`(V^(2) )/(R_i)` -----------------let this be equation 2

P₁ = V²/R₁

P₁ = 4P₂

so

P₁ = V²/R₁ = 4( V²/R² )

now, form the above equation;

R₁ = R₂/4

using equation 1, we get;

P₁ =
`I^(2) . R_1`

P₂ =
`I^(2) . R_2`

Hence;

P₁ =
`I^(2)`( R₂/4)

P₁ =
`I^(2)` × ( R₂/4)

P₁ = (1/4) P₂ or 0.25

Therefore; the ratio P₁/P₂ of their power dissipations is 0.25