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
Explanation:
Given the data in the question;
[tex]P_{i}[/tex] = [tex]I^{2} . R_i[/tex] --------------let this be equation 1
[tex]P_{i}[/tex] = [tex]\frac{V^{2} }{R_i}[/tex] -----------------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 = [tex]I^{2} . R_1[/tex]
P₂ = [tex]I^{2} . R_2[/tex]
Hence;
P₁ = [tex]I^{2}[/tex]( R₂/4)
P₁ = [tex]I^{2}[/tex] × ( R₂/4)
P₁ = (1/4) P₂ or 0.25
Therefore; the ratio P₁/P₂ of their power dissipations is 0.25
