Question

A student has been given 3 resistances of 3 ohms each.
(a) How should he connect these resistances so as to obtain a resultant resistance of 1 ohm?
(b) Draw a labelled diagram to show the combination of these resistances.

Answer 1

(a) He should connect all the three resistances in a parallel connection. Then the net resistance of the parallel combination will be 1 ohm.

$$\begin{gathered} \frac{1}{R_{\mathrm{net}}}=\frac{1}{R_1}+\frac{{\displaystyle 1}}{{\displaystyle R_2}}+\frac{{\displaystyle 1}}{{\displaystyle R_3}}=\frac{1}{3}+\frac{{\displaystyle 1}}{{\displaystyle 3}}+\frac{{\displaystyle 1}}{{\displaystyle 3}} \\ \Rightarrow \frac{{\displaystyle 1}}{{\displaystyle R_{\mathrm{net}}}}=\frac{3}{3}=1\mathrm{\Omega } \\ \Rightarrow R_{\mathrm{net}}\mathit{=}1\mathit{}\mathrm{\Omega } \end{gathered}$$

(b) All three given resistors connected in parallel: