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Study of Capacitors in Series and Parallel Circuits

Capacitor: Stores electrical energy in the form of an electric field between its plates. The capacitance 𝐶 C is given by

𝐶 = 𝑄 𝑉 C= V Q

where 𝑄 Q = charge stored, 𝑉 V = voltage across capacitor.

Series Connection:

1 𝐶 𝑒 𝑞 = 1 𝐶 1 + 1 𝐶 2 + 1 𝐶 3 + … C eq

= C 1

+ C 2

+ C 3

+…

(Equivalent capacitance decreases; total is less than the smallest capacitor).

Parallel Connection:

𝐶 𝑒 𝑞 = 𝐶 1 + 𝐶 2 + 𝐶 3 + … C eq

=C 1

+C 2

+C 3

+…

(Equivalent capacitance increases; total is the sum of all).

Charging/Discharging: When a capacitor charges through a resistor:

𝑉 𝑐 ( 𝑡 ) = 𝑉 ( 1 − 𝑒 − 𝑡 / 𝑅 𝐶 ) V c

(t)=V(1−e −t/RC )

When discharging:

𝑉 𝑐 ( 𝑡 ) = 𝑉 𝑒 − 𝑡 / 𝑅 𝐶 V c (t)=Ve −t/RC

where 𝑅 𝐶 RC is the time constant (in seconds).

To verify the relationship of equivalent capacitance for capacitors connected in series and in parallel.

To measure the charging and discharging behavior of a capacitor through a resistor.

To compare experimental results with theoretical values.

DC Power Supply / Battery (6–12 V)

Capacitors (e.g., 10 µF, 22 µF, 47 µF)

Resistor (1 kΩ – 10 kΩ for charging/discharging)

Voltmeter (or Digital Multimeter)

Stopwatch (or oscilloscope for accurate time measurement)

Connecting wires, breadboard, switch

Part A: Capacitors in Series

Connect capacitors 𝐶 1 , 𝐶 2 , 𝐶 3 C 1

,C 2

,C 3

in series across the supply.

Measure voltage across the combination and across each capacitor.

Calculate 𝐶 𝑒 𝑞 C eq

theoretically and compare with measured.

Part B: Capacitors in Parallel

Connect capacitors 𝐶 1 , 𝐶 2 , 𝐶 3 C 1

,C 2

,C 3

in parallel.

Measure voltage across each capacitor (should be equal to supply voltage).

Calculate and compare 𝐶 𝑒 𝑞 C eq

(theoretical vs measured).

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