Answer:
r=0.127
Explanation:
When connected in series
Current = I
When connected in parallel
Current = 10 I
We know that equivalent resistance
In series R = R₁+R₂
in parallel R= R₁R₂/(R₂+ R₁)
Given that voltage is constant (Vo)
V = I R
Vo = I (R₁+R₂) ------------1
Vo = 10 I (R₁R₂/(R₂+ R₁)) -------2
From above equations
10 I (R₁R₂/(R₂+ R₁)) = I (R₁+R₂)
10 R₁R₂ = (R₁+R₂) (R₂+ R₁)
10 R₁R₂ = 2 R₁R₂ + R₁² + R₂²
8 R₁R₂ = R₁² + R₂²
Given that
r = R₁/R₂
Divides by R₂²
8R₁/R₂ = ( R₁/R₂)²+ 1
8 r = r ² + 1
r ² - 8 r+ 1 =0
r= 0.127 and r= 7.87
But given that R₂>R₁ It means that r<1 only.
So the answer is r=0.127
