Series-connected circuit elements are shown in the figure below.

Which of the vectors shown represents the total impedance?

To find the answer, we must first understand that impedances of RLC components in series add together, shown in the following formula:

$Z_{total}=Z_R+Z_L+Z_C$

Therefore, we can write the total impedance of this circuit as:

$Z_{total} = \left(30\Omega \right)+\left(j90\Omega \right)-\left(j50\Omega \right)$

When adding complex numbers written in rectangular form, we must add together the real parts and separately add together the imaginary parts of the equation:

$Z_{total} = \left(30\Omega \right)+(j90\Omega - j50\Omega )$

$Z_{total} = 30\Omega +j40\Omega$

30Ω is the real part of our impedance, while j40Ω is the imaginary part of our impedance. Since the X-axis represents the real part and the Y-axis represents the imaginary part, and being that both real and imaginary parts of our total impedance are positive, then our vector must fall in the 1st quadrant of the graph.

Therefore, A  represents the total impedance of this RLC circuit.