Two capacitors, of capacitance C, are connected in series. If one of them is filled with a dielectric substance K, what is the effective capacitance?

Updated On: Jun 25, 2024

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Solution and Explanation

When two plates of a capacitor are separated by a dielectric medium with a dielectric constant K, the capacitance Cm can be determined using the equation Cm=Kε0dA, which can also be expressed as Cm=KC0=KC, where C0=C is the original capacitance.
Now, when two capacitors, KC and C, are arranged in series, the effective capacitance ′C′ is given by:
C′1=KC1+C1
This can be further simplified as:
C′1=K1(C1+C1)=K1⋅C2=KC2
Rearranging, we get:
2C′=2KC
Hence, the effective capacitance C′ for capacitors KC and C in series is 2C′=2KC.

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