High School Physics : Calculating Total Capacitance

Study concepts, example questions & explanations for High School Physics

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Example Questions

Example Question #2 : Capacitors

Three capacitors are in series. They have capacitances of \(\displaystyle 3F\)\(\displaystyle 2F\), and \(\displaystyle 8F\), respectively. What is their total capacitance?

Possible Answers:

\(\displaystyle 0.958F\)

\(\displaystyle 1.11F\)

\(\displaystyle 13F\)

\(\displaystyle 1.04F\)

\(\displaystyle 0.077F\)

Correct answer:

\(\displaystyle 1.04F\)

Explanation:

For capacitors in series the formula for total capacitance is:

\(\displaystyle \frac{1}{C_{eq}}=\frac{1}{C_1}+\frac{1}{C_2}+\frac{1}{C_3}...\)

Note that this formula is similar to the formula for total resistance in parallel. Using the values for each individual capacitor, we can solve for the total capacitance.

\(\displaystyle \frac{1}{C_{eq}}=\frac{1}{3F}+\frac{1}{2F}+\frac{1}{8F}\)

\(\displaystyle \frac{1}{C_{eq}}=0.958F\)

\(\displaystyle C_{eq}=1.04F\)

Example Question #1 : Calculating Total Capacitance

Three capacitors are in parallel. They have capacitance values of \(\displaystyle 3F\)\(\displaystyle 2F\), and \(\displaystyle 8F\). What is their total capacitance?

Possible Answers:

\(\displaystyle 0.958F\)

\(\displaystyle 13F\)

\(\displaystyle 0.077F\)

\(\displaystyle 1.04F\)

\(\displaystyle 1.09F\)

Correct answer:

\(\displaystyle 13F\)

Explanation:

For capacitors in parallel the formula for total capacitance is:

\(\displaystyle C_{eq}=C_1+C_2+C_3...\)

Note that this formula is similar to the formula for total resistance in series. Using the values for each individual capacitor, we can solve for the total capacitance.

\(\displaystyle C_{eq}=3F+2F+8F\)

\(\displaystyle C_{eq}=13F\)

Example Question #3 : Capacitors

Three capacitors, each with a capacity of \(\displaystyle 4F\) are arranged in parallel. What is the total capacitance of this circuit?

Possible Answers:

\(\displaystyle 1.33F\)

\(\displaystyle 0.08F\)

\(\displaystyle 64F\)

\(\displaystyle 12F\)

\(\displaystyle 0.75F\)

Correct answer:

\(\displaystyle 12F\)

Explanation:

The formula for capacitors in parallel is:

\(\displaystyle C_{eq}=C_1+C_2+C_3...\)

Our three capacitors all have equal capacitance values. We can simply add them together to find the total capacitance.

\(\displaystyle C_{eq}=4F+4F+4F\)

\(\displaystyle C_{eq}=12F\)

Example Question #4 : Calculating Total Capacitance

What is the total capacitance of a series circuit with capacitors of \(\displaystyle 5F\)\(\displaystyle 1.1F\), and \(\displaystyle 7.5F\)?

Possible Answers:

\(\displaystyle 1.2F\)

\(\displaystyle 0.07F\)

\(\displaystyle 4.5F\)

\(\displaystyle 13.6F\)

\(\displaystyle 0.8F\)

Correct answer:

\(\displaystyle 0.8F\)

Explanation:

The total capacitance of a series circuit is \(\displaystyle \frac{1}{C_{eq}}=\frac{1}{C_1}+\frac{1}{C_2}+\frac{1}{C_3}...\)

Plug in our given values.

\(\displaystyle \frac{1}{C_{eq}}=\frac{1}{C_1}+\frac{1}{C_2}+\frac{1}{C_3}...\)

\(\displaystyle \frac{1}{C_{eq}}=\frac{1}{5F}+\frac{1}{1.1F}+\frac{1}{7.5F}\)

\(\displaystyle \frac{1}{C_{eq}}=1.24F\)

\(\displaystyle C_{eq}=0.8F\)

Example Question #1 : Capacitors

Calculate the total capacitance of a circuit with the following three capacitors in parallel.

\(\displaystyle C_1=10F,\ C_2=15F,\ C_3=5F\)

Possible Answers:

\(\displaystyle 3.21F\)

\(\displaystyle 2.73F\)

\(\displaystyle 5F\)

\(\displaystyle 30F\)

\(\displaystyle 15F\)

Correct answer:

\(\displaystyle 30F\)

Explanation:

To calculate the total capacitance for capacitors in parallel, simply sum the value of each individual capacitor.

\(\displaystyle C_{eq}=C_1+C_2+C_3\)

\(\displaystyle C_{eq}=10F+15F+5F=30F\)

Example Question #4 : Calculating Total Capacitance

Calculate the total capacitance of a circuit with the following three capacitors in series.

\(\displaystyle C_1=10F,\ C_2=15F,\ C_3=5F\)

Possible Answers:

\(\displaystyle 2.73F\)

\(\displaystyle 3.12F\)

\(\displaystyle 25F\)

\(\displaystyle 0.367F\)

\(\displaystyle 30F\)

Correct answer:

\(\displaystyle 2.73F\)

Explanation:

To find the total capacitance for capacitors in series, we must sum the inverse of each individual capacitance and take the reciprocal of the result.

\(\displaystyle \frac{1}{C_{eq}}=\frac{1}{C_{1}}+\frac{1}{C_{2}}+\frac{1}{C_{3}}\)

\(\displaystyle \frac{1}{C_{eq}}=\frac{1}{10F}+\frac{1}{15F}+\frac{1}{5F}\)

\(\displaystyle \frac{1}{C_{eq}}=\frac{11}{30}=0.367\)

Remember, you must still take the final reciprocal!

\(\displaystyle C_{eq}=\frac{30}{11}=2.73F\)

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