The value of
R₁/R₂ is 5 : 9.For the given network, the effective resistance between A and B is R₁ and between A and D is R₂.
We have to find the value of R₁/R₂.
Case 1 : effective resistance between A and B = R₁
Here we see, two resistors of same resistance R are joined in series.
∴ r' = R + R = 2R
Now, two resistors of resistance R, four resistors of resistance 2R are joined in series.
∴ r'' = R + R + 2R + 2R + 2R + 2R = 10R
Now, r' and r'' are joined in parallel.
∴ effective resistance, R₁ = r'r''/(r' + r'') = (2R × 10R)/(2R + 10R) = (5/3)R
Case 2 : effective resistance between A and D = R₂
A to C, there are four resistors of same resistance R and from C to D, one resistor of resistance 2R are joined in series.
∴ R' = R + R + R + R + 2R = 6R
from A - F - E - D , there are three resistors of same resistance 2R are joined in series.
∴ R'' = 2R + 2R + 2R = 6R
Now, R' and R'' are joined in parallel.
∴ effective resistance, R₂ = R'R''/(R' + R'') = (6R × 6R)/(6R + 6R) = 3R
Therefore the value of R₁/R₂ is (5/3)R/3R = 5/9.
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