Question

How will you connect three resistors of 2 Ω, 3 Ω and 5 Ω respectively so as to obtain a resultant of 2.5 Ω? Draw the diagram to show the arrangement.

Answer 1

To get the resistance of 2.5 Ώ, we will have to connect the resistors of values 2 Ώ and 3 Ώ in series and this arrangement should be connected in parallel with the resistor of value 5 Ώ.


$$\begin{gathered} \mathrm{Resistance}2\mathrm{\Omega }\mathrm{and}3\mathrm{\Omega }\mathrm{are}\mathrm{in}\mathrm{series}\mathrm{their}\mathrm{net}\mathrm{resistance}\mathrm{is} \\ R=R_1+R_2 \\ R=2\mathrm{\Omega }+3\mathrm{\Omega } \\ R=5\mathrm{\Omega } \\ \mathrm{This}5\mathrm{\Omega }\mathrm{resistance}\mathrm{is}\mathrm{in}\mathrm{parallel}\mathrm{with}\mathrm{another}5\mathrm{\Omega }\mathrm{resistance}\mathrm{therefore}\mathrm{their}\mathrm{net}\mathrm{resistance}is:\text{'} \\ \frac{1}{R}=\frac{1}{R_1}+\frac{1}{R_2} \\ \frac{1}{R}=\frac{1}{5}+\frac{1}{5} \\ \frac{1}{R}=\frac{2}{5} \\ R=2.5\mathrm{\Omega }\mathrm{Hence},\mathrm{net}\mathrm{resistance}\mathrm{of}\mathrm{the}\mathrm{combination}\mathrm{will}\mathrm{be}2.5\mathrm{\Omega } \end{gathered}$$