A) \[9.42\,\times {{10}^{4}}\,m\]
B) \[18\,\times 8.\,{{10}^{4}}m\]
C) \[4.5\,\times {{10}^{4}}\,m\]
D) none of these
Correct Answer: A
Solution :
Key Idea: When inductive reactance is equal to capacitive reactance circuit is in resonance. In an L-C circuit the impedance of circuit is \[Z={{X}_{L}}-{{X}_{C}}\] When \[{{X}_{L}}={{X}_{C}},\]then \[~Z=0.\]In this situation the amplitude of current in the circuit would be infinite. It will be condition of electrical resonance and frequency is given by \[f=\frac{1}{2\pi \sqrt{LC}}\] \[=\frac{1}{2\times 3.14\times \sqrt{10\times {{10}^{-3}}\times 0.25\times {{10}^{-6}}}}\] \[=3184.7\,\]cycles/s. Also frequency \[\text{=}\,\frac{\text{velocity}}{\text{wavelength}}\] \[\Rightarrow \] \[\lambda =\frac{c}{f}=\frac{3\times {{10}^{8}}}{3184.7}\] \[\Rightarrow \] \[\lambda =9.42\times {{10}^{4}}m\]You need to login to perform this action.
You will be redirected in
3 sec