Three unequal resistors in parallel are equiv | vedclass

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(B) Let the three resistances be $R_1, R_2$ and $R_3$. Given that $\frac{R_1}{R_2} = \frac{1}{2}$,we can write $R_1 = k$ and $R_2 = 2k$. For resistors

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$(b)$ $6$

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(B) Let the three resistances be $R_1, R_2$ and $R_3$. Given that $\frac{R_1}{R_2} = \frac{1}{2}$,we can write $R_1 = k$ and $R_2 = 2k$. For resistors in parallel,the equivalent resistance $R_{eq}$ is given by $\frac{1}{R_{eq}} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3}$. Substituting the given values,$\frac{1}{1} = \frac{1}{k} + \frac{1}{2k} + \frac{1}{R_3}$. Rearranging for $R_3$,we get $\frac{1}{R_3} = 1 - (\frac{1}{k} + \frac{1}{2k}) = 1 - \frac{3}{2k} = \frac{2k-3}{2k}$. Thus,$R_3 = \frac{2k}{2k-3}$. Since $R_3$ must be a positive integer and all resistors must be unequal: If $k=1$,$R_3 = -2$ (impossible). If $k=2$,$R_1=2, R_2=4, R_3=4$ (not unequal). If $k=3$,$R_1=3, R_2=6, R_3=\frac{6}{3} = 2$. Here,$R_1=3, R_2=6, R_3=2$. All are unequal and integers. The largest resistance is $6 \ \Omega$.

Three unequal resistors in parallel are equivalent to a resistance $1 \ \Omega$. If two of them are in the ratio $1:2$ and if no resistance value is fractional,then the largest of the three resistances in ohms is

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