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### College Physics (Urone)

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.

See the step by step solution

## Step 1: Combination of series resistance

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.

## Step 2: Calculation of the second resistance

(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${\mathrm{R}}_{2}=-400\mathrm{k\Omega }$.

## Step 3: Unreasonable about the result

(b)

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

## Step 4: Inconsistence assumption

(c)

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