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) 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)`

Answer

B, C

Explanation

(b,c) : Impedance of the RC circuit is given by the following relation:
`Z= sqrt(R^(2)+(1)/(omega^(2)C^(2)))`
When dielectric is inserted in case B then capacitance increases and hence impedance of the circuit decreases . So current in case B increases . Hence option ( b)is correct.
Due to increase in current voltage across the resistor increases and thus voltage across capacitor decreases because voltages are related as `V= sqrt(V_(R)^(2)+V_(C)^(2))`. Hence option ( c ) is correct.