Calculating Total Capacitance - High School Physics

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Question

Three capacitors are in series. They have capacitances of , , and , respectively. What is their total capacitance?

Answer

For capacitors in series the formula for total capacitance is:

$\frac{1}{C_{eq}}=\frac{1}{C_1}+\frac{1}{C_2}+\frac{1}{C_3}...$

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.

$\frac{1}{C_{eq}}=\frac{1}{3F}+\frac{1}{2F}+\frac{1}{8F}$

$\frac{1}{C_{eq}}=0.958F$

$C_{eq}=1.04F$

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Question

Three capacitors are in parallel. They have capacitance values of , , and . What is their total capacitance?

Answer

For capacitors in parallel the formula for total capacitance is:

$C_{eq}=C_1+C_2+C_3...$

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.

$C_{eq}=3F+2F+8F$

$C_{eq}=13F$

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Question

Three capacitors, each with a capacity of are arranged in parallel. What is the total capacitance of this circuit?

Answer

The formula for capacitors in parallel is:

$C_{eq}=C_1+C_2+C_3...$

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

$C_{eq}=4F+4F+4F$

$C_{eq}=12F$

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Question

What is the total capacitance of a series circuit with capacitors of , , and ?

Answer

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

Plug in our given values.

$\frac{1}{C_{eq}}=\frac{1}{C_1}+\frac{1}{C_2}+\frac{1}{C_3}...$

$\frac{1}{C_{eq}}=\frac{1}{5F}+\frac{1}{1.1F}+\frac{1}{7.5F}$

$\frac{1}{C_{eq}}=1.24F$

$C_{eq}=0.8F$

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Question

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

$C_1=10F,\ C_2=15F,\ C_3=5F$

Answer

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

$C_{eq}=C_1+C_2+C_3$

$C_{eq}=10F+15F+5F=30F$

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Question

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

$C_1=10F,\ C_2=15F,\ C_3=5F$

Answer

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.

$\frac{1}{C_{eq}}=\frac{1}{C_{1}}+\frac{1}{C_{2}}+\frac{1}{C_{3}}$

$\frac{1}{C_{eq}}=\frac{1}{10F}+\frac{1}{15F}+\frac{1}{5F}$

$\frac{1}{C_{eq}}=\frac{11}{30}=0.367$

Remember, you must still take the final reciprocal!

$C_{eq}=\frac{30}{11}=2.73F$

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