Chapter 23.1, Problem 17PP

To determine

The value of resistance to be use to reduce the resistance in the branch.

Answer to Problem 17PP

  $244.73\Omega$ resistor should be added in parallel.

Explanation of Solution

Given:

The resistance in the branch, $R=150\Omega$

It is to be reduced to, $R_n=93\Omega$

Formula used:

In parallel combination of resistors, the net resistance is,

  $\frac{1}{R_n}=\frac{1}{R_1}+\frac{1}{R_2}$

Calculation:

To reduce the net resistance in the branch, a new resistance must be added in parallel to the system. The value of new resistance to be added must be,

  $\begin{array}{l}\frac{1}{R_n}=\frac{1}{R_1}+\frac{1}{R_2}\\ \frac{1}{93}=\frac{1}{150}+\frac{1}{R_2}\\ R_2=244.73\Omega \end{array}$

Conclusion:

Hence, the $244.73\Omega$ should be added in parallel to the given resistor.