Questions: Module 2 Homework Begin Date: 8/26/2024 12:01:00 AM Due Date: 9/9/2024 11:59:00 PM End Date: 9/10/2024 11:59:00 PM Problem 6: (13% of Assignment Value) Three capacitors and a battery are connected as shown. The capacitance values are C1=9.6 μF, C2=5.2 μF, and C3=7.8 μF. The battery voltage is V0=12 V. Part (a) Enter an expression for the equivalent capacitance, C12, of the two capacitors C1 and C2 in terms of the variables given in the problem statement. C12=

Module 2 Homework
Begin Date: 8/26/2024 12:01:00 AM Due Date: 9/9/2024 11:59:00 PM End Date: 9/10/2024 11:59:00 PM
Problem 6: (13% of Assignment Value)
Three capacitors and a battery are connected as shown. The capacitance values are C1=9.6 μF, C2=5.2 μF, and C3=7.8 μF. The battery voltage is V0=12 V.

Part (a)
Enter an expression for the equivalent capacitance, C12, of the two capacitors C1 and C2 in terms of the variables given in the problem statement.
C12=

Transcript text: Module 2 Homework Begin Date: 8/26/2024 12:01:00 AM Due Date: 9/9/2024 11:59:00 PM End Date: 9/10/2024 11:59:00 PM Problem 6: ( $13 \%$ of Assignment Value) Three capacitors and a battery are connected as shown. The capacitance values are $C_{1}=9.6 \mu \mathrm{F}$, $C_{2}=5.2 \mu \mathrm{F}$, and $C_{3}=7.8 \mu \mathrm{F}$. The battery voltage is $V_{0}=12 \mathrm{~V}$. Part (a) Enter an expression for the equivalent capacitance, $C_{12}$, of the two capacitors $C_{1}$ and $C_{2}$ in terms of the variables given in the problem statement. \[ C_{12}= \]

Solution

Solution Steps

Step 1: Identify the Configuration of Capacitors

The capacitors $ C_1 $ and $ C_2 $ are connected in parallel. In a parallel configuration, the equivalent capacitance $ C_{12} $ is the sum of the individual capacitances.

Step 2: Write the Formula for Equivalent Capacitance in Parallel

For capacitors in parallel, the equivalent capacitance $ C_{12} $ is given by: \[ C_{12} = C_1 + C_2 \]

Step 3: Substitute the Given Values

Given: \[ C_1 = 9.6 \, \mu\text{F} \] \[ C_2 = 5.2 \, \mu\text{F} \]

Substitute these values into the formula: \[ C_{12} = 9.6 \, \mu\text{F} + 5.2 \, \mu\text{F} \]