Question

The alternating voltage and current in an electric circuit are respectively given by $E=100\sin 100\pi t,I=5\sin 100\pi t$. The reactance of the circuit will be :

• A. $1\Omega$
• B. $0.05\Omega$
• C. $20\Omega$
• D. Zero

Answer 1

Answer: (C)

$20\Omega$

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

$E=E_0\sin \omega t$ ....(i)

$I=I_0\sin \omega t$ ....(ii)

Given that,

$E=100\sin 100\pi t$ ....(iii)

$I=5\sin 100\pi t$ ....(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

$E_{rms}=\frac{E_0}{\sqrt{2}}=\frac{100}{\sqrt{2}}V$

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

$I_{rms}=\frac{I_0}{\sqrt{2}}=\frac{5}{\sqrt{2}}A$

Hence, reactance of the circuit is given by

$Z=\frac{E_{rms}}{I_{rms}}=\frac{\frac{100}{\sqrt{2}}}{\frac{5}{\sqrt{2}}}=20\Omega$