The equivalent capacitance of the combination shown in the figure is
\(\frac{3C}{2}\)
3C
2C
\(\frac{C}{2}\)
The Correct Option is C
Solution and Explanation
To find the equivalent capacitance of the given combination, we will analyze the arrangement of capacitors shown in the image.
In the diagram, we have:
- Two capacitors \( C \) in parallel with each other.
- These parallel capacitors are in series with another capacitor \( C \).
Let's calculate the equivalent capacitance of the system.
Step 1: Calculate the capacitance for the parallel arrangement
The formula for the equivalent capacitance \( C_p \) for capacitors in parallel is:
\(C_p = C_1 + C_2\)
Thus, for the two capacitors in parallel:
\(C_p = C + C = 2C\)
Step 2: Calculate the total capacitance with the series capacitor
The formula for the equivalent capacitance \( C_s \) for capacitors in series is:
\(\frac{1}{C_s} = \frac{1}{C_p} + \frac{1}{C_3}\)
Substitute the given values:
\(\frac{1}{C_s} = \frac{1}{2C} + \frac{1}{C}\)
\(\frac{1}{C_s} = \frac{1 + 2}{2C} = \frac{3}{2C}\)
Thus, \(C_s = \frac{2C}{3}\)
Conclusion
The equivalent capacitance of the combination is \(C_s = 2C\). Therefore, the correct answer is \(2C\).
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Concepts Used:
Combination of Capacitors
The total capacitance of this equivalent single capacitor depends both on the individual capacitors and how they are connected. There are two simple and common types of connections, called series and parallel, for which we can easily calculate the total capacitance.
Read Also: Combination of Capacitors
Series capacitors
When one terminal of a capacitor is connected to the terminal of another capacitors , called series combination of capacitors.
Capacitors in Parallel
Capacitors can be connected in two types which are in series and in parallel. If capacitors are connected one after the other in the form of a chain then it is in series. In series, the capacitance is less.
When the capacitors are connected between two common points they are called to be connected in parallel.
When the plates are connected in parallel the size of the plates gets doubled, because of that the capacitance is doubled. So in a parallel combination of capacitors, we get more capacitance.
Read More: Types of Capacitors