Five capacitors each of capacitance value c are connected
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Five capacitors, each of capacitance value C are connected as shown in the figure. The ratio of capacitance between P and R,
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The capacitors having same charge through them would be in the series combination. If the source is connected between P and R, same charge would pass through 2 capacitors in the arms QR and PQ.
At the same time, similar charge would flow through the capacitors in the arms TS, PT and SK. Hence, equivalent capacitance of left side C=C×C/C+C=C/2 and equivalent capacitance of right side 1/C=1/C+1/C+1/C=3/C. Hence C=C/3.
As, C and C will in parallel combination, we can write, C1=C+C=C/2+C/3=5C/6. If any source is connected between points P and Q, then the equivalent capacitance must be C2=C+C/4 = 5C/4.
Therefore, required ratio is given by C1/C2 = (5C/6)/(5C/4)=2/3.
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