Physics - Current Electricity Question with Solution | TestHub

Let the resistances be$R_1, R_2$and$R_3$

$\therefore \frac{R_1}{R_2}=\frac{1}{2}⟹R_1=k, R_2=2k$

In parallel$\frac{1}{R}=\frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_3}$

$\frac{1}{1}=\frac{1}{k}+\frac{1}{2k}+\frac{1}{R_3}$

$\frac{1}{R_3}=1-\frac{1}{k}=\frac{1}{2k}$

$=\frac{2k-2-1}{2k}=\frac{2k-3}{2k}$

$R_3=\frac{2k}{2k-3}$

If k = 1, then$R_3$is found to be negative, which is impossible.

If k = 2, then$R_1=2, R_2=4 R_3=4$

$R_2=R_3$, not satisfying the condition of the question that all resistance are unequal.

$If k=3, \mathrm{t}\mathrm{h}\mathrm{e}\mathrm{n} R_1=3, R_2=6$

$R_3=\mathrm{2 }\mathrm{\Omega }$

∴ Largest resistance$=\mathrm{6 }\mathrm{\Omega }\mathrm{ }$