In a series LRC circuit, which quantity is the same through the resistor, inductor, and capacitor?

State the impedance magnitude of a series LRC circuit.

State the phase-angle relation for a series LRC circuit.

A series circuit has \(R=30\,\Omega\), \(X_L=80\,\Omega\), and \(X_C=40\,\Omega\). Find \(Z\).

A series LRC circuit has \(Z=60\,\Omega\) and source voltage \(120\,\mathrm V\) rms. Find the rms current.

A series circuit has \(R=20\,\Omega\), \(X_L=70\,\Omega\), and \(X_C=45\,\Omega\). Find \(\phi\) and state whether the circuit is inductive or capacitive.

A series circuit has \(I_{\mathrm{rms}}=2.0\,\mathrm A\), \(R=10\,\Omega\), \(X_L=50\,\Omega\), and \(X_C=20\,\Omega\). Find \(V_R\), \(V_L\), and \(V_C\).

Using the circuit in the previous question, find the source rms voltage.

A series circuit has \(R=40\,\Omega\), \(L=0.20\,\mathrm H\), \(C=50\,\mu\mathrm F\), and \(f=50\,\mathrm{Hz}\). Find \(Z\).

Derive why the series LRC impedance uses \(X_L-X_C\), not \(X_L+X_C\).