Chapter 19, Problem 8P

To determine

The possible values of resistance in different combinations.

Answer to Problem 8P

The possible values of resistance are $25\Omega$ , $35\Omega$ , $60\Omega$ , and $14.58\Omega$ .

Explanation of Solution

Given information:

Resistance of the first register, $R_1=25\Omega$

Resistance of the second register $R_2=35\Omega$

Formula used:

Write the expression to calculate the total resistance of the circuit in series connection.

  $R_{\text{S}}=R_1+R_2$............(1)

Where,

• The total resistance of the circuit is $R_{\text{S}}$ in series connection.

Write the expression to calculate the total resistance of the circuit in parallel connection.

  $\frac{1}{R_{\text{P}}}=\frac{1}{R_1}+\frac{1}{R_2}$........... (2)

Where,

• The total resistance of the circuit is $R_{\text{P}}$ in parallel connection.

Calculation:

Substitute the values in equation (1).

  $\begin{array}{c}{R}_{\text{S}}=25+35\\ =60\Omega \end{array}$

Substitute the values in equation (2).

  $\begin{array}{c}\frac{1}{R_{\text{P}}}=\frac{1}{25}+\frac{1}{35}\\ R_{\text{P}}=\frac{25\times 35}{25+35}\\ =\frac{875}{60}\\ =14.58\Omega \end{array}$

The possible value of resistance also can be obtained when each resister is considered alone.

Therefore, the possible values of resistance are

  $25\Omega$ , $35\Omega$ , $60\Omega$ , and $14.58\Omega$ .