Four identical condensers are connected in parallel and then in series equivalent capacitance in series to that in parallel combination is
Four identical condensers are connected in parallel and then in series equivalent capacitance in series to that in parallel combination is
- 16 : 1
- 4 : 1
- 1 : 4
- 1 : 16
The Correct Option is D
Solution and Explanation
Let's denote the capacitance of each individual capacitor as C. Then, the equivalent capacitance in parallel, Cp, is given by:
Cp = 4C
Now, when capacitors are connected in series, the reciprocal of the equivalent capacitance is equal to the sum of the reciprocals of the individual capacitances.
For our case, since we have four identical capacitors connected in series, the equivalent capacitance in series, Cs, is given by:
\(\frac {1}{C_s}\) = \(\frac {1}{C}\) + \(\frac {1}{C}\)+ \(\frac {1}{C}\) + \(\frac {1}{C}\)
\(\frac {1}{C_s}\) = \(\frac {4}{C}\)
Taking the reciprocal of both sides, we get:
Cs = \(\frac {C}{4}\)
Therefore, the ratio of the equivalent capacitance in series to that in the parallel combination is:
\(\frac {C_s}{C_p }\)= \(\frac {\frac {C}{4}}{4C}\)
\(\frac {C_s}{C_p } \) = \(\frac {1}{16}\)
The correct answer is (D) 1 : 16.
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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