Ac Circuits

Step 1: Identify circuit condition.
Given that , the inductive and capacitive reactances cancel each other. Hence, the circuit operates at resonance.
Step 2: Calculate total impedance.
At resonance, the net reactance is zero and the impedance is purely resistive:

Step 3: Calculate circuit current.

Step 4: Voltage across the capacitor.

Step 5: Phase angle of capacitor voltage.
The voltage across a capacitor lags the current by . Hence,

Step 6: Final conclusion.
Therefore, the rms voltage across the capacitor is V.

Step 1: Recall Delta to Wye conversion formula.
In a Delta ( ) connected circuit, if each branch has impedance , then the equivalent Wye (Y) impedance is given by:

Step 2: Substitute the given value.
It is given that each branch of the Delta circuit has impedance:

Substituting into the formula:

Step 3: Simplify the expression.

Step 4: Match with the given options.
The obtained result matches option (A).
Step 5: Final conclusion.
Hence, each branch of the equivalent Wye circuit has impedance .