A series combination of circuit elements X and Y is connected across AC mains. The current is ahead of voltage by a phase difference of `pi` /3 radians . The element Y is a resistor of 150 `Omega` . Name the circuit element X. Calculate the rms value of current if rms value of voltage is 150 V.

Explanation

The circuit element X is a capacitor as the current is ahead of voltage.
Given phase angle `Phi = (pi)/(3)`
cos `Phi = (R )/(Z )`
where R is the resistance of element X and Z is the impedance of the circuit .
R = 150 `Omega`
`cos""(pi)/(3) = (150)/(Z)`
`Z = (150)/(cos""(pi)/(3))= 150 xx2 = 300 Omega`
rms value of current in the circuit is
`I_("rms") = (epsilon_("rms"))/(Z)`
Given ` epsilon_("rms") = 150 V `
`implies I_("rms") = (150)/(300)=0.5 A `