question_answer

A\[1\mu F\]capacitor is charged to 50 V potential difference and then discharged through a 10 mH inductor of negligible resistance. The maximum current in the inductor will be

A)  0.5 A           

B)  1.6 A

C)  0.16 A          

D)  1.0 A

Correct Answer: A

Solution :

 When a charged capacitor is allowed to discharge through a resistance inductor electrical oscillations of constant amplitude are produced in the circuit. These are called \[L-C\]oscillations. The energy stored in charged capacitor is \[U=\frac{1}{2}C{{V}^{2}}=\frac{1}{2}L{{i}^{2}}\] where,\[i\]is current in the circuit and V the potential difference. \[\therefore \] \[i=\sqrt{\frac{C}{L}}V\] Given,  \[C=1\mu F=1\times {{10}^{-6}}F,\] \[L=10mH=10\times {{10}^{-3}}H\] \[V=50V\] \[\therefore \] \[i=\sqrt{\frac{1\times {{10}^{-6}}}{10\times {{10}^{-3}}}}\times 50=0.5A\]