In a circuit, an inductor (L), capacitor (C) and resistor (R) are connected in parallel across a source of emf given by `epsilon=epsilon_(0) sin omega t`. Find the current through the mains and draw a phasor diagram.

Options

A. `(sqrt3)/(|omegaC - (1)/(omegaL)|)`
B. `sqrt3|(1)/(omegaC) - omegaL|`
C. `sqrt5|(1)/(omegaC) - omegaL|`
D. None of these

Answer

A

Explanation

`(i_(R_(0)))/(sqrt(i_(R0)^(2) + (i_(c0) - i_(L0)))) = (1)/(2)`
`Rightarrow (epsilon_(0)/(R))/(sqrt((epsilon_(0)/(R)^(2)) + (epsilon_(0)omegaC - (epsilon_(0))/(omegaL))^(2))) = (1)/(2)`
`Rightarrow R = (sqrt3)/(omegaC - (1)/(omegaL))`