We show that the maximum or minimum impedance of a special parallel RLC studied in a previous paper can be found analytically, without using calculus. In fact, we show that the maximum or minimum value occurs when the driving frequency is equal to o 1/ LC , a fact that was determined graphically in that previous paper. Furthermore, we show that either the maximum or minimum value is given by 2 2 R 1 3 ,where L/C / R. Also, for the minimum impedance 2 min Z R 1 2 / 3 3 R/ 3, whereas for the maximum impedance 2 max Z R 1 2/ R.
Latin American Journal of Physics Education
Cartwright, K. and E. Kaminsky, “Determining the maximum or minimum impedance of a special parallel RLC circuit without calculus,” Latin-American J. Phys. Educ., vol. 6, no. 1, March 2012, pp. 55-58.