The general equations of alternating voltage and current in an AC circuit are as follows
E=E0sinωt ....(i)
I=I0sinωt ....(ii)
Given that,
E=100sin100πt ....(iii)
I=5sin100πt ....(iv)
Comparing equations (ii) and (iv), we get,
Peak value of current, I0=5A
Comparing equations (i) and (iii), we get
Peak value of voltage, E0=100V
Now, r.m.s. value of voltage is given by
Erms=E0√2=100√2V
Similarly, r.m.s. value of current is given by
Irms=I0√2=5√2A
Hence, reactance of the circuit is given by
Z=ErmsIrms=100√25√2=20Ω