Calculate the total capacitance of the circuit

Question

ScanSolve AI Tutor · Accepted Answer

To calculate the total capacitance of the circuit, we need to identify the series and parallel combinations of the capacitors.

Identify the capacitors in series.
The 20 $\mu$ F capacitor and the 60 $\mu$ F capacitor are connected in series.
The formula for two capacitors in series is $\frac{1}{C_{series}} = \frac{1}{C_1} + \frac{1}{C_2}$ or $C_{series} = \frac{C_1 C_2}{C_1 + C_2}$ .
Calculate the equivalent capacitance of the series combination.
$C_{series} = \frac{20 \, \mu\text{F} \times 60 \, \mu\text{F}}{20 \, \mu\text{F} + 60 \, \mu\text{F}}$ $C_{series} = \frac{1200 \, (\mu\text{F})^2}{80 \, \mu\text{F}}$ $C_{series} = 15 \, \mu\text{F}$
Identify the parallel combination.
The equivalent series capacitance ( $C_{series} = 15 \, \mu\text{F}$ ) is in parallel with capacitor 'X'.
The formula for capacitors in parallel is $C_{total} = C_{eq} + C_X$ .
Formulate the total capacitance.
The total capacitance of the circuit is the sum of the equivalent series capacitance and capacitor 'X'.
$C_{total} = C_{series} + C_X$ $C_{total} = 15 \, \mu\text{F} + C_X$
The value for capacitor 'X' is not provided in the diagram. Therefore, a numerical value for the total capacitance cannot be calculated.

The total capacitance is $\boxed{15 \, \mu\text{F} + C_X}$ where $C_X$ is the capacitance of capacitor X.

Answer