The impedance of an RLC series circuit is 8 ohms at resonance when f = 60hz but the impedance changes to 10 ohms when the frequency is increased to f = 80hz. Calculate the values of Capacitance, C and Inductance, L of the circuit.
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This won't be a full solution, but should get you started. Refer http://hyperphysics.phy-astr.gsu.edu/hbase/electric/rlcser.html for the basic equations:
At resonance, you have w0 = 1/sqrt(LC). We know w0 is 60, so you have one equation with 2 variables.
At resonance, the circuit impedance of a series RLC circuit is just R so you now know that.
In general, the impedance of a series RLC circuit is Z = sqrt(R^2 + (XL - XC)^2), where XL = 1/wL and XC = 1/wC. The second half tells you Z at 80Hz, so this falls out to another equation in L and C.
Solving the two equations in L and C for positive values (it's a safe assumption you don't have negative capacitance or impedance) gives a simple quadratic, which you should be able to solve in the normal manner.