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Q13PE

Expert-verifiedFound in: Page 775

Book edition
1st Edition

Author(s)
Paul Peter Urone

Pages
1272 pages

ISBN
9781938168000

**Two resistors, one having a resistance of${\mathbf{900}}{\mathbf{}}{\mathbf{k\Omega}}$, are connected in series to produce a total resistance of ${\mathbf{0}}{\mathbf{.}}{\mathbf{5}}{\mathbf{}}{\mathbf{M\Omega}}$. (a) What is the value of the second resistance? (b) What is unreasonable about this result? (c) Which assumptions are unreasonable or inconsistent?**

(a)The value of the second resistance is${\mathrm{R}}_{2}=-400\mathrm{k\Omega}$.

(b)Value of the second resistor is negative.

(c)Resistance of the series is less than the resistance of the single resistor.

**The resultant resistance of series combination resistors is given as,**

**${{\mathbf{R}}}_{{\mathbf{s}}}{\mathbf{=}}{{\mathbf{R}}}_{{\mathbf{1}}}{\mathbf{+}}{{\mathbf{R}}}_{{\mathbf{2}}}$**

**Here, ${{\mathbf{R}}}_{{\mathbf{s}}}$is the resultant resistance for series combination, ${{\mathbf{R}}}_{{\mathbf{1}}}$and ${{\mathbf{R}}}_{{\mathbf{2}}}$are the resistances of the resistors connected in series.**

**(a)**

Resistors value in series adds up. That means that:

${\mathrm{R}}_{2}={\mathrm{R}}_{\mathrm{s}}-{\mathrm{R}}_{1}\phantom{\rule{0ex}{0ex}}=0.5\mathrm{M\Omega}-900\mathrm{k\Omega}\phantom{\rule{0ex}{0ex}}=0.5\mathrm{M\Omega}\left(\frac{1000\mathrm{k\Omega}}{1\mathrm{M\Omega}}\right)-900\mathrm{k\Omega}\phantom{\rule{0ex}{0ex}}=-400\mathrm{k\Omega}$

Therefore, the value of the second resistance is${\mathrm{R}}_{2}=-400\mathrm{k\Omega}$.

**(b)**

The unreasonable result is: negative value of the second resistor.

**(c)**

The assumptions are unreasonable or inconsistent is, resistance of the series is less than the resistance of the single resistor.

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