Chapter 19, Problem 10P

To determine

The method of connection of the resistor.

Answer to Problem 10P

The required voltage can be obtained by using four resistors of $1\Omega$ in the series connection.

Explanation of Solution

Given info:

Voltage of the battery, $V=6\text{V}$

Voltage required to apply, $V_2=4\text{V}$

Resistors connected to supply, $R_1=1\Omega$

Formula Used:

To obtain the required voltage there should be voltage drop across resistor. The voltage drop across each resistor in parallel connection remain same but voltage drop takes place in series connection of the resistors and same current passes through each resistor.

The expression to calculate the voltage in the series circuit is,

  $V=I{R}_e$      .......(1)

Here,

  $R_e$ is the equivalent voltage and its value is $6\Omega$ .

The expression to calculate the required voltage by same current in the battery is,

  $R=\frac{V_2}{I}$       .......(2)

The expression to calculate the number of resistor required to obtain required voltage is,

  $n=\frac{R}{R_1}$      .......(3)

Calculation:

Unlimited supply can be given to across resistor for battery voltage. Substitute all the values in the expression (1) to calculate the current in the circuit.

  $\begin{array}{c}6\text{V}=I\left(6\Omega \right)\\ I=1\text{A}\end{array}$

Substitute all the values in the expression (2) to obtain the resistance.

  $\begin{array}{c}R=\frac{4\text{V}}{1\text{A}}\\ =4\Omega \end{array}$

Substitute all the values in the expression (3) to obtain the number of resistance.

  $\begin{array}{c}n=\frac{4\Omega }{1\Omega }\\ =4\end{array}$

Conclusion:

Therefore, the required voltage can be obtained by using four resistors of $1\Omega$ in series connection.