A sereis R-C circuit is connected to AC voltage source. Consider two cases, (A) when C is without a dielectric medium and (B) when C is filled with dielectric of constant 4. The current `I_(R)` through the resistor and voltage `V_(c)` across the capacitor are compared in the two cases. Which of the following is/ are true?

Options

A. `I_(R)^(A)gtI_(R)^(B)`
B. `I_(R)^(A)ltI_(R)^(B)`
C. `V_(C)^(A)ltV_(C)^(B)`
D. None of these

Answer

B

Explanation

For circuit A
Impedence,`Z_(A)=sqrt(R^(2+1))/(omega^(2)C^(2))`
Potential difference across C,
`V_(C)^(A)=(I_(R)^(A)xx(1))/(omegaC)=(V)/(sqrt(RomegaC)^(2)+1)`
For circuit B
Impedence,`Z_(B)=sqrt(R^(2)+(1))/(4omega^(2)C^(2))
Potential difference across C,
`V_(C)^(B)=(I_(R)^(B)xx(1))/(4omegaC)=(V)/(sqrt(4RomegaC)^(2)+1))`
Hence from above Eqs (i) and (ii) we conclude that
`I_(R)^(B)gtI_(R)^(B)and V_(C)^(A)gtV_(C)^(B)`