Question

Two resistors, one having a resistance of $\mathbf{145}\mathbf{\Omega }$, are connected in parallel to produce a total resistance of $\mathbf{150}\mathbf{\Omega }$. (a) What is the value of the second resistance? (b) What is unreasonable about this result? (c) Which assumptions are unreasonable or inconsistent?

Short answer

(a)The value of the second resistance is$-4350\Omega$.

(b)Negative value of resistance.

(c)Resistance of parallel series is in between values of separate resistors.

Step-by-step solution

Combination of parallel resistance

The resultant resistance of parallel combination resistors is given as,

$\frac{\mathbf{1}}{{\mathbf{R}}_{\mathbf{p}}}\mathbf{=}\frac{\mathbf{1}}{{\mathbf{R}}_{\mathbf{1}}}\mathbf{+}\frac{\mathbf{1}}{{\mathbf{R}}_{\mathbf{2}}}$

Here, ${\mathbf{R}}_{\mathbf{p}}$is the resultant resistance for parallel combination, ${\mathbf{R}}_{\mathbf{1}}$and ${\mathbf{R}}_2$are the resistances of the resistors connected in parallel.

Calculation of the second resistance

(a)

Resistance of one of the resistors in parallel session can be calculated as:

$$\begin{gathered} R_2=\frac{R_p{R}_1}{R_{p}R} \\ =\frac{145\Omega \times 150\Omega }{145\Omega -150\Omega } \\ =-4350\Omega \end{gathered}$$

Therefore, the value of the second resistance is${\mathrm{R}}_2=-4350\mathrm{\Omega }$.

Unreasonable about the result

(b)

This result is unreasonable because of negative value of resistance, which is not possible.

Inconsistence assumption

(c)

The assumptions are unreasonable or inconsistent is, resistance of parallel series is in between values of separate resistors.