Question

Two resistors r1 & r2 (r1 < r2 ) are joined in parallel. The equivalent resistance R is such that (1) R > r1 + r2 (2) r2 < R < r1 + r2 (3) r1 + R < r2 (4) R < r

Answer 1

Dear Student,
When two resistors r1 and r2 are joined in parallel combination to give equivalent resistance R we get-
$$\begin{gathered} \frac{1}{R}=\frac{1}{r1}+\frac{1}{r2} \\ \frac{1}{R}=\frac{r1+r2}{r1r2} \\ R=\frac{r1r2}{r1+r2} \\ ifr1=r2=r \\ R=\frac{r^2}{2r}=\frac{r}{2} \\ ItmeansR<r \end{gathered}$$
Thus in case of parallel combination the equivalent resistance (R) is always less than the individual resistance i.e. r1 and r2.
Regards