# If a maximum resistance produced by two resistors is 5 Omega and minimum resistance produced by them is 1.2 Omega, then what is the value of the resistances?

Nov 25, 2016

The maximum resistance is when the two resistances are in series, and the minimum when they are in parallel

#### Explanation:

${R}_{1} + {R}_{2} = 5 \Omega$

$\frac{{R}_{1} {R}_{2}}{{R}_{1} + {R}_{2}} = 1.2 \Omega$

Solve the system and find:

${R}_{1} = 2 \Omega$
${R}_{1} = 3 \Omega$

Nov 25, 2016

${r}_{1} = 2$ and ${r}_{2} = 3$

#### Explanation:

The maximun resistance is with both in series

${r}_{1} + {r}_{2} = 5$

and the minimum is when in parallel

$\frac{1}{r} _ 1 + \frac{1}{r} _ 2 = \frac{1}{1.2}$ so

$\left\{\begin{matrix}{r}_{1} + {r}_{2} = 5 \\ \frac{{r}_{1} + {r}_{2}}{{r}_{1} {r}_{2}} = \frac{1}{1.2}\end{matrix}\right.$

or

$\left\{\begin{matrix}{r}_{1} + {r}_{2} = 5 \\ {r}_{1} {r}_{2} = 1.2 \times 5\end{matrix}\right.$ giving

${r}_{1} = 2$ and ${r}_{2} = 3$
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