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12 Nov 2019
In some experiments, short distances are measured by using capacitance. Consider forming an LC circuit using a parallel-plate capacitor with plate area A, and a known inductance L. (a) If charge is found to oscillate in this circuit at frequency f = OMEGA/2 Pi when the capacitor plates are separated by distance .x,. show that x = A pi A 0 f 2 L. (b) When the plate separation is changed by Delta. x. the circuit's oscillation frequency will change by Delta f. Show that Delta. x/.x g 2(Delta f/f). (c) If f is on the order of I MHz and can be measured to a precision of Delta f = 1 Hz, with what percent accuracy can x be determined? Assume fringing effects at the capacitor's edges can be neglected.
In some experiments, short distances are measured by using capacitance. Consider forming an LC circuit using a parallel-plate capacitor with plate area A, and a known inductance L. (a) If charge is found to oscillate in this circuit at frequency f = OMEGA/2 Pi when the capacitor plates are separated by distance .x,. show that x = A pi A 0 f 2 L. (b) When the plate separation is changed by Delta. x. the circuit's oscillation frequency will change by Delta f. Show that Delta. x/.x g 2(Delta f/f). (c) If f is on the order of I MHz and can be measured to a precision of Delta f = 1 Hz, with what percent accuracy can x be determined? Assume fringing effects at the capacitor's edges can be neglected.
Casey DurganLv2
12 Nov 2019