NEET-XII-Physics
39: Alternating Current
- #16-aWhat frequency should be chosen to maximise the current in the circuit? (b) What is the value of this maximum current?Ans : In an LCR circuit, current is maximum when reactance is minimum, which occurs at resonance, i.e. when capacitive reactance becomes equal to the inductive reactance,i.e.
XL = XC
`` \Rightarrow \omega L=\frac{1}{\omega C}``
`` \Rightarrow {\omega }^{2}=\frac{1}{LC}=\frac{1}{2\times 18\times {10}^{-6}}``
`` \Rightarrow {\omega }^{2}=\frac{{10}^{6}}{36}``
`` \Rightarrow \omega =\frac{{10}^{3}}{6}``
`` \Rightarrow 2\,\mathrm{\,\pi \,}f=\frac{{10}^{3}}{6}``
`` \Rightarrow f=\frac{1000}{6\times 2\,\mathrm{\,\pi \,}}=26.539\,\mathrm{\,Hz\,}``
`` =27\,\mathrm{\,Hz\,}`` (b) At resonance, reactance is minimum.
Minimum Reactance, Z = R
Maximum current (I) is given by,
`` I=\frac{E}{R}``
`` \Rightarrow I\mathit{=}\frac{20}{10\times {10}^{3}}``
`` \Rightarrow I=\frac{2\,\mathrm{\,A\,}}{{10}^{3}}=2\,\mathrm{\,mA\,}``
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- #16-bWhat is the value of this maximum current?Ans : At resonance, reactance is minimum.
Minimum Reactance, Z = R
Maximum current (I) is given by,
`` I=\frac{E}{R}``
`` \Rightarrow I\mathit{=}\frac{20}{10\times {10}^{3}}``
`` \Rightarrow I=\frac{2\,\mathrm{\,A\,}}{{10}^{3}}=2\,\mathrm{\,mA\,}``
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