Question

What is the resultant resistance of the three resistors of 5 Ω, 4 Ω and 10 Ω connected as shown in the figure? What is this combination of resistors known as?

Answer 1

This given combination of resistors is known as parallel combination.

In a parallel combination, the reciprocal of the resultant resistance is equal to the sum of reciprocals of the individual resistances present in the combination. For the three resistors connected in parallel,

$\because \frac{1}{R_{\mathrm{Resultant}}}=\frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_3}$

$$\begin{gathered} \Rightarrow \frac{1}{R_{\mathrm{Resultant}}}=\frac{1}{5\mathrm{\Omega }}+\frac{1}{4\mathrm{\Omega }}+\frac{1}{10\mathrm{\Omega }}=\frac{11}{20\mathrm{\Omega }} \\ \Rightarrow R_{\mathrm{Resultant}}=\frac{20}{11}\mathrm{\Omega } \end{gathered}$$