Question

the current vs. frequency plots of two circuits having the same inductance and capacitance , but the different resistance is shown above. which of the two circuits will have a higher resistance?

Answer 1

The graph plots are not visible.  however we can say the following.

Impedance of the series alternating current circuit with an inductance, resistance, capacitances is given as  follows:

   I = V / Z                  Z = impedance
                             I , V are RMS values or peak values.

 $Z= \sqrt{R^2+(\omega L - \frac{1}{\omega C})^2}\\\\Let\ \omega_0=\frac{1}{\sqrt{LC}}\\\\Z=\sqrt{R^2+\frac{1}{C}(\frac{1}{\omega_0}-\frac{1}{\omega})^2}$

If L and C are same then ω₀ is same between two circuits.  Which ever circuit has higher resistance, will have higher impedance for the same frequency ω.

At ω = ω₀,  Z = R,  and hence, look at this frequency where the current vs frequency graph reaches a peak.    I_max = V / R    as Z = R at this resonance frequency.

Hence, which ever circuit has higher peak current at resonance, has lower resistance in the circuit.