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High School Physics : Using Capacitor Equations

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Example Questions

Example Question #2 : Capacitors

Three capacitors in parallel have a capacity of $\displaystyle 2F$, 12F $\displaystyle 12F$, and $\displaystyle 8F$, respectively. What is the total capacitance?

Possible Answers:

0.045F $\displaystyle 0.045F$

22F $\displaystyle 22F$

1.41F $\displaystyle 1.41F$

4.23F $\displaystyle 4.23F$

7.33F $\displaystyle 7.33F$

Correct answer:

22F $\displaystyle 22F$

Explanation:

The formula for capacitors in parallel is:

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

Plug in our given values:

$C_{eq}=2F+12F+8F$ $\displaystyle C_{eq}=2F+12F+8F$

$C_{eq}=22F$ $\displaystyle C_{eq}=22F$

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Example Question #4 : Capacitors

Three capacitors in series have a capacity of $\displaystyle 2F$, 12F $\displaystyle 12F$, and $\displaystyle 8F$, respectively. What is the total capacitance?

Possible Answers:

0.71F $\displaystyle 0.71F$

7.33F $\displaystyle 7.33F$

0.45F $\displaystyle 0.45F$

22F $\displaystyle 22F$

1.41F $\displaystyle 1.41F$

Correct answer:

1.41F $\displaystyle 1.41F$

Explanation:

The formula for capacitors in series is:

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

Plug in our given values:

$\frac{1}{C_{eq}}=\frac{1}{2F}+\frac{1}{12F}+\frac{1}{8F}$ $\displaystyle \frac{1}{C_{eq}}=\frac{1}{2F}+\frac{1}{12F}+\frac{1}{8F}$

$\frac{1}{C_{eq}}=0.70833\frac{1}{F}$ $\displaystyle \frac{1}{C_{eq}}=0.70833\frac{1}{F}$

$C_{eq}=1.41F$ $\displaystyle C_{eq}=1.41F$

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Example Question #1 : Using Capacitor Equations

Three capacitors of equal capacitance are in a series circuit. If the total capacitance is 12F $\displaystyle 12F$, what is the capacitance of each individual capacitor?

Possible Answers:

36F $\displaystyle 36F$

$\displaystyle 4F$

$\frac{1}{4}F$ $\displaystyle \frac{1}{4}F$

$\frac{1}{36}F$ $\displaystyle \frac{1}{36}F$

$\displaystyle 3F$

Correct answer:

36F $\displaystyle 36F$

Explanation:

The formula for capacitors in a series is:

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

Since we have three equal capacitors, we can say:

$\frac{1}{C_{eq}}=\frac{1}{C}+\frac{1}{C}+\frac{1}{C}=3*\frac{1}{C}$ $\displaystyle \frac{1}{C_{eq}}=\frac{1}{C}+\frac{1}{C}+\frac{1}{C}=3*\frac{1}{C}$

Using the value for total capacitance, we can find the value for the individual capacitance.

$\frac{1}{C_{eq}}=\frac{3}{C}$ $\displaystyle \frac{1}{C_{eq}}=\frac{3}{C}$

$\frac{1}{12F}=\frac{3}{C}$ $\displaystyle \frac{1}{12F}=\frac{3}{C}$

36F=C $\displaystyle 36F=C$

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Example Question #2 : Using Capacitor Equations

Three capacitors of equal capacitance are in a parallel circuit. If the total capacitance is 12F $\displaystyle 12F$, what is the capacitance of each individual capacitor?

Possible Answers:

$\displaystyle 3F$

$\displaystyle 4F$

$\frac{1}{12}F$ $\displaystyle \frac{1}{12}F$

$\frac{1}{36}F$ $\displaystyle \frac{1}{36}F$

12F $\displaystyle 12F$

Correct answer:

$\displaystyle 4F$

Explanation:

The formula for capacitors in parallel is:

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

Since we have three equal capacitors, we can say:

$C_{eq}=C+C+C=3C$ $\displaystyle C_{eq}=C+C+C=3C$

Use the value for total capacitance to find the individual capacitance value.

$C_{eq}=3C$ $\displaystyle C_{eq}=3C$

12F=3C $\displaystyle 12F=3C$

$\frac{12F}{3}=C$ $\displaystyle \frac{12F}{3}=C$

4F=C $\displaystyle 4F=C$

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High School Physics : Using Capacitor Equations

Study concepts, example questions & explanations for High School Physics

All High School Physics Resources

Example Questions

Example Question #2 : Capacitors

Example Question #4 : Capacitors

Example Question #1 : Using Capacitor Equations

Example Question #2 : Using Capacitor Equations

All High School Physics Resources

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