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+//===========================================================================
+//chapter 9 example 4
+clc;
+clear all;
+
+//variable declaration
+f1 = 60; //frequency in Hz
+f2 = 50; //frequency in Hz
+C1 = 10^-6; //inductance of circuit
+R1 = 100; //resistance in Ω
+C2 = 1.5*10^-6; //capacitance
+
+//calculations
+L1 = 1/(4*((%pi)^2)*((f1)^2)*C1); //inductance of circuit in H
+w = 2*%pi*f2;
+Z1 = R1+(%i)*((w*L1)-(1/(w*C1))); //impedance of circuit at 50 Hz Ω
+//Z2 = R1+(%i)*((w*L2)-(1/(w*C2))); //impedance of circuit at 50 Hz Ω
+//real(Z2) = real(Z1)
+//((w*L2)-(1/(w*C2))) = real(Z1)=963
+x =abs((w*L1)-(1/(w*C1)))
+y = 1/(w*C2);
+L2 =(x+y)/w;
+z = sqrt(1/(L2*C2));
+f2 = (1/(2*%pi))*(z);
+
+//result
+mprintf("resonant frequency of circuit = %3.1f Hz",f2);