A capacitor stores 10 µC charge when connected across a battery. When the gap between the plates is filled with a dielectric, a charge of 20 µC flows through the battery. Find the dielectric constant of the dielectric.
Answer & explanation
Correct answer: option 1
The correct answer is Option 2: k = 2
- Initial charge = 10 μC
- Final charge = 20 μC
- Dielectric constant (k) = Final charge / Initial charge
In absence of dielectric
Q = CV = 10 µC . . . (1)
With dielectric
Q' = kCV = 20 µC . . . (2)
From (i) and (2)
k = 2
Key Idea: When a dielectric is inserted, capacitance increases ⇒ charge increases (since battery remains connected)