physics

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The general equations of alternating voltage and current in an AC circuit are as follows

$E=E_{0}sinωt$ ....(i)

$I=I_{0}sinωt$ ....(ii)

Given that,

$E=100sin100πt$ ....(iii)

$I=5sin100πt$ ....(iv)

Comparing equations (ii) and (iv), we get,

Peak value of current, $I_{0}=5A$

Comparing equations (i) and (iii), we get

Peak value of voltage, $E_{0}=100V$

Now, r.m.s. value of voltage is given by

$E_{rms}=2 E_{0} =2 100 V$

Similarly, r.m.s. value of current is given by

$I_{rms}=2 I_{0} =2 5 A$

Hence, reactance of the circuit is given by

$Z=I_{rms}E_{rms} =2 5 2 100 =20Ω$

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