The equivalent capacitance of the arrangement shown in the figure is:

Question image

Understand the Problem

The question is asking for the equivalent capacitance of a specific arrangement of capacitors shown in a figure. It presents several answer options to choose from, which involves applying principles of electrical circuits, particularly the combination of capacitors.

Answer

The equivalent capacitance is $20 \, \mu F$.
Answer for screen readers

The equivalent capacitance of the arrangement is $20 , \mu F$.

Steps to Solve

  1. Identify the configuration of capacitors

In the circuit, we have three capacitors of $15 , \mu F$ each on the left side in series and one $15 , \mu F$ capacitor on the right side in parallel with them.

  1. Calculate the equivalent capacitance for the series group

The formula for capacitors in series is given by:

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

For three capacitors of $15 , \mu F$:

$$ \frac{1}{C_{eq, series}} = \frac{1}{15} + \frac{1}{15} + \frac{1}{15} = \frac{3}{15} $$

Therefore, the equivalent capacitance for the series group is:

$$ C_{eq, series} = \frac{15}{3} = 5 , \mu F $$

  1. Add the parallel capacitor's capacitance

Next, we add the equivalent capacitance of the series group to the capacitance of the parallel capacitor. The formula for capacitors in parallel is:

$$ C_{eq, total} = C_{eq, series} + C_{parallel} $$

So,

$$ C_{eq, total} = 5 , \mu F + 15 , \mu F = 20 , \mu F $$

The equivalent capacitance of the arrangement is $20 , \mu F$.

More Information

In this arrangement of capacitors, the connection type affects the equivalent capacitance significantly. For series combinations, the total capacitance decreases, while for parallel combinations, it increases.

Tips

  • Forgetting the difference between series and parallel configurations can lead to errors in calculation.
  • Not simplifying the fractions correctly when calculating equivalent capacitance for capacitors in series.
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