A) \[9.42\times {{10}^{4}}\] m
B) \[18.8\times {{10}^{4}}\] m
C) \[4.5\times {{10}^{4}}\] m
D) None
Correct Answer: A
Solution :
In an LC-circuit, the impedance of circuit is given by \[Z={{X}_{L}}-{{X}_{C}}\] When \[{{X}_{L}}={{X}_{C}}\] then Z = 0. In this situation, the amplitude s of current in the circuit would be infinite. It will be condition of electrical resonance and frequency is given by: \[f=\frac{1}{2\pi \sqrt{LC}}\,\] \[=\frac{1}{2\times 3.14\,\times \sqrt{10\times {{10}^{-3}}\,\times 0.25\,\times {{10}^{-6}}}}\] \[=3184.7\,\,cycle\,{{s}^{-1}}\] Also, frequency \[=\frac{velocity}{wavelength}\] \[\Rightarrow \,\lambda =\frac{c}{f}\,=\frac{3\times {{10}^{8}}}{318.7}\,=9.42\,\times {{10}^{4}}m\]
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