Chapter 19, Problem 76GP

To determine

The number of resistance, value of each resistance and method of connection of resistors.

Answer to Problem 76GP

The number of resistor is 7, value of resistance of each resistor is $0.3143\text{kΩ}$ and resistors must be connected in series connection.

Explanation of Solution

Given info:

The power across single resistor is, $p=\frac{1}{2}\text{W}$ .

The equivalent power across all resistors is, $P=3.5\text{W}$ .

The equivalent resistance is, $R_e=2.2\text{kΩ}$ .

Formula Used:

The expression to calculate the number of the resistors is,

  $n=\frac{P}{p}$

The expression to calculate the value of each resistor is,

  $R=\frac{R_e}{n}$

Calculation:

Substitute all the values in the above expression.

  $\begin{array}{c}n=\frac{3.5\text{W}}{\frac{1}{2}\text{W}}\\ =7\end{array}$

Substitute all the values in the above expression.

  $\begin{array}{c}R=\frac{2.2\text{kΩ}}{7}\\ =0.3143\text{kΩ}\end{array}$

The equivalent resistance in the parallel connection remain always lower than each resistance of the parallel connection but in the series connection, the equivalent resistance remain always greater than the each resistance of the series connection.

Conclusion:

Thus, the number of resistor is 7, value of resistance of each resistor is $0.3143\text{kΩ}$ and resistors must be connected in series connection.