===== R–L–C Series Resonant Circuit =====

==== Background information ====
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**“Resonance describes the oscillatory response of a system when it is excited by a frequency that matches or is close to the system’s natural frequency.”**
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The resonance frequency is given by:
$$f_{\rm r} = \frac{1}{2\pi \sqrt{LC}}\text{, or} ~~~ \omega_{\rm r} = \frac{1}{\sqrt{LC}}$$
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At resonance, the current is given by:
$$I = \frac{U}{R}$$
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==== Experimental Tasks ====
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  - Set up the following measurement circuit: {{drawio>Fig-7_V4-R–L–C-Series-resonant-circuit.svg}}\\ <WRAP centeralign> <imgcaption Fig-7_V4-R–L–C-Series-resonant-circuit | R–L–C Series Resonant Circuit> </imgcaption> </WRAP> \\ The corresponding phasor diagram is shown in <imgref Fig-7_V4-R–L–C-Series-resonant-circuit>. \\
  - The function generator shall be set to produce a sinusoidal signal, and the amplitude of the output voltage shall be 6 V. For the circuit shown above, the magnitude of the impedance is given by: $$Z = \sqrt{R^2 + (\omega L − \frac{1}{\omega C})^2}$$ \\ As can be seen from <imgref Fig-7_V4-R–L–C-Series-resonant-circuit>, the inductive and capacitive voltage components partially cancel each other. There exists a specific frequency at which these components cancel completely, causing the circuit to behave as a purely resistive circuit. This frequency is known as the resonance frequency. \\
  - Calculate the resonance frequency for the assembled measurement circuit. \\ (The capacitance of the capacitor is determined using a measuring instrument) \\ \\ $f_{\rm r}~=~ ..........................................................$ \\ \\
  - Adjust the frequency of the function generator so that the ratio $\frac{f}{f_{\rm r}}$ corresponds to the values listed in <tabref Table-2-R–L–C_Resonant_V4>. 
  - Measure the RMS voltage $U_{\rm R}$ using the oscilloscope and record the measured values in <tabref Table-2-R–L–C_Resonant_V4>. {{drawio>Table-2-R–L–C_Resonant_V4.svg}}\\ <tabcaption Table-2-R–L–C_Resonant_V4 | R-L-C-circuit RMS voltage> </tabcaption> \\
  - **Plot the current as a function of the ratio $\frac{f}{f_{\rm r}}$ on a logarithmic scale.**

==== Test questions - Resonant Circuit ====