Question
Physics Question on electrostatic potential and capacitance
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?
Answer
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 =Kε 0 dA , which can also be expressed as Cm =KC 0=KC , where C 0=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=KC 1+C 1
This can be further simplified as:
C ′1=K 1(C 1+C 1)=K 1⋅ C 2=KC 2
Rearranging, we get:
2 C ′=2 KC
Hence, the effective capacitance C ′ for capacitors KC and C in series is 2 C ′=2 KC .