Using Capacitor Equations

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Physics › Using Capacitor Equations

Questions 1 - 4

1

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

$\frac{1}{36}F$

$\frac{1}{4}F$

Explanation

The formula for capacitors in a series is:

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

Since we have three equal capacitors, we can say:

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

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

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

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

2

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

$\frac{1}{12}F$

$\frac{1}{36}F$

Explanation

The formula for capacitors in parallel is:

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

Since we have three equal capacitors, we can say:

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

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

$C_{eq}=3C$

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

3

Three capacitors in series have a capacity of , , and , respectively. What is the total capacitance?

Explanation

The formula for capacitors in series is:

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

Plug in our given values:

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

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

$C_{eq}=1.41F$

4

Three capacitors in parallel have a capacity of , , and , respectively. What is the total capacitance?

Explanation

The formula for capacitors in parallel is:

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

Plug in our given values:

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

$C_{eq}=22F$

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