A series `R-C` circuit is connected to an alternating voltage source. Consider two situations
(a) When capacitor is air filled.
(b) When capacitor is mica filled.
current through resistor is `i` and voltage across capacitor is `V` then

Options

A. `V_(a)=V_(b)`
B. `V_(a) lt V_(b)`
C. `V_(a) gt V_(b)`
D. `i_(a) gt i_(b)`

Answer

C

Explanation

`X_(C)=(1)/(2pifC)`
current in circuit
`I=(V)/(Z)=(V)/(sqrt(R^(2)+((1)/(2pifC))^(2)))`
or `1=(2pifC)/(sqrt(4pi^(2)f^(2)C^(2)R^(2)+1))xxV`
voltage drop acroos capacitor
`V_(C)=IxxX_(C)`
`=(2pifCxxV)/(sqrt(4pi^(2)f^(2)C^(2)R^(2)+1))xx(1)/(2pifC)`
`V_(C)=(V)/(sqrt(4pi^(2)f^(2)C^(2)R^(2)+1))`
When mica is introduced capacitance will increase, hence voltage across capacitor gets decrease.