Chapter 19, Problem 37P

To determine

The net capacitance of the circuit.

Answer to Problem 37P

The voltage across first capacitor in series connection is $14.86\text{V}$ , the voltage across first capacitor in series connection is $11.14\text{V}$ and the voltage across third capacitor in series connection is $26\text{V}$ .

Explanation of Solution

Given info:

The capacitance of the capacitors in series are, $C_1,C_2=3\text{μF},4\text{μF}$ .

The capacitance of the capacitors in parallel is, $C_3=2\text{μF}$ .

Formula Used:

The expression to calculate the charge across capacitors in series connection is,

  $Q=\left(\frac{C_1{C}_2}{C_1+C_2}\right)V$

The expression to calculate the voltage across first capacitor in series connection is,

  $V_1=\frac{Q}{C_1}$

The expression to calculate the voltage across second capacitor in series connection is,

  $V_2=\frac{Q}{C_2}$

Calculation:

Substitute all the values in the above expression.

  $\begin{array}{c}Q=\left[\frac{\left(3\text{μF}\right)\left(4\text{μF}\right)}{3\text{μF}+4\text{μF}}\right]\left(26\text{V}\right)\\ =44.57\text{μC}\end{array}$

Substitute all the values in the above expression.

  $\begin{array}{c}{V}_1=\frac{44.57\text{μC}}{3\text{μF}}\\ =14.86\text{V}\end{array}$

Substitute all the values in the above expression.

  $\begin{array}{c}{V}_2=\frac{44.57\text{μC}}{4\text{μF}}\\ =11.14\text{V}\end{array}$

The voltage across parallel capacitor is same as the applied voltage.

Conclusion:

Therefore, the voltage across first capacitor in series connection is $14.86\text{V}$ , the voltage across first capacitor in series connection is $11.14\text{V}$ and the voltage across third capacitor in series connection is $26\text{V}$ .