When an AC source of `emf e=E_(0) sin(100t)` is connected across a circuit i in the circuit, the phase difference between the emf e and the current i in the circuit is observed to be `(pi//4)`, as shown in the diagram. If the circuit consists possibly only of R-C or R-L or L-C in series, find the relationship between the two elements

Options

A. `R = 1 k Omega , C = 10 mu F `
B. `R = 1 k Omega, C = 1 mu F `
C. `R = 1 k Omega, L = 10 H`
D. `R = 1 k Omega , L = 1 H`

Answer

A

Explanation

`tan phi = (X_(L))/(R) " or " tan phi = (X_(C))/(R)`
`{:(rArr 1 = (omega L)/(R), " "1 = (1)/(omega CR) ),(rArr R = omega L, " "rArr omega CR = 1 ):}`
Since, current leads voltage,
Then for capacitive circuit here `omega CR = 1`
Now, from the options
`rArr 100 xx 10 xx 10^(-6) xx 10^(3) = 1 `
`1 = 1 rArr LHS = RHS`