### Long Question Solution

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#### Kinematics

Introduction to Kinematics

# Capacitance - Long Question Answer 5

Question: Three capacitors are arranged in such a way that two capacitors are connected in series and across them a third capacitor is connected in parallel combination. Find the net capacitance if the combination of the three.

Answer: In the given figure (i) two capacitors C1 and C2 are connected in series and these series are connected in parallel with a capacitor of capacitance C3.

The total capacitance of C` of C1 and C2 in series is given by;
1/C` = 1/C1 + 1/C2
C` = C12 / C1 + C2

This capacitance C`is parallel to C3 as shown inf figure (ii). Let C be the total capacitance of capacitors C` and C3 in parallel, such that
C = C` + C3
C = (C12 / C1 + C2) + C3
C = (C1C2 + C2C3 + C3C1)/ C1 + C­2

This is the required expression for the net capacitance of three capacitors arranged in such a way that two capacitors are connected in series and across them a third capacitor is connected in parallel combination.

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