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A sereis R-C circuit is connected to AC ...

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?

A

`I_(R )^(A) gt I_(R )^(B)`

B

`I_(R )^(A) lt I_(R )^(B)`

C

`V_(C )^(A) gt V_(C)^(B)`

D

`V_(C )^(A) lt V_(C)^(B)`

Text Solution

Verified by Experts

The correct Answer is:
B, C
Case (A): `Z_(A)=sqrt(R^(2)+((1)/(omega C))^(2))`
case (B) `Z_(B)=sqrt(R^(2)+((1)/(omega K C))^(2))`
so, `Z_(B)ltZ_(A)`
`I_(R )^(A)=V/(Z_A)` and `I_(R )^(B) = V/(Z_B) clearly `I_(R )^(A) lt I_(R )^(B)`.
Since currnet in case (B) is greater so, p.d. across R will increases in case(B) and thus across capacitor will decrease.
Hence `V_(C )^(A) gt V_(C)^(B)`. `(V_(R )^(2)+V_(C )^(2)=V_(0)^(2))` .
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