(II) In some experiments, short distances are measured
Chapter , Problem 33(choose chapter or problem)
(II) In some experiments, short distances are measured byusing capacitance. Consider forming an LC circuit using aparallel-plate capacitor with plate area A, and a knowninductance L. (a) I f charge is found to oscillate in this circuitat frequency / = o i/lir when the capacitor plates areseparated by distance x, show that x = 4ir2A e 0f 2L.(b) When the plate separation is changed by Ax, the circuitsoscillation frequency w ill change by A f. Show thatA x /x ~ 2(A/ / / ) . (c) I f / is on the order of 1 MHz and canbe measured to a precision of A f = 1 Hz, with whatpercent accuracy can x be determined? Assume fringingeffects at the capacitors edges can be neglected.
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