Chapter 19, Problem 7P

To determine

The voltage across the $2200\Omega$ resistor.

Answer to Problem 7P

The voltage across the $2200\Omega$ resistor is $9.26\text{V}$ .

Explanation of Solution

Given information:

Resistance of the first register, $R_1=650\Omega$

Resistance of the second register $R_2=2200\Omega$

Voltage across the battery, $V=12\text{V}$

Formula used:

Write the expression to calculate the current in the circuit when both registers are connected in series using Kirchhoff Voltage Law.

  $-V+I{R}_1+I{R}_2=0$............. (1)

Where,

• The current in the circuit is $I$ .

Write the expression to calculate the voltage across register $R_2$ .

  $V_2=I{R}_2$

Where,

• The voltage across register $R_2$ is $V_2$ .

Calculation:

Substitute the value in equation (1).

  $\begin{array}{l}-12+I\times 650+I\times 2200=0\\ I=\frac{12}{650+2200}\\ =4.20\times {10}^{-3}\text{A}\end{array}$

Substitute the value of the current in equation (2).

  $\begin{array}{c}{V}_2=4.20\times {10}^{-3}\times 2200\\ \approx 9.26\text{V}\end{array}$

Therefore, the voltage across the $2200\Omega$ resistor is $9.26\text{V}$ .