## Related questions with answers

Consider that an emf is connected to a parallel $R L C$ circuit. In this case, the voltage $V_{\max }$ is the same across the source and each element, but the net current is the sum of the individual currents, so a phasor diagram for the currents can be drawn instead. Draw this diagram. By dividing the magnitude of each current phasor by the common value of $V_{\max }$, obtain a phasor diagram that relates impedance, reactances, and resistance. Use the geometry of the diagram to show that

$Z=\left[\frac{1}{R^2}+\left(\frac{1}{X_L}-\frac{1}{X_C}\right)^2\right]^{-1 / 2}$

Solution

VerifiedIn this problem, we have a parallel RLC circuit connected to a source with an amplitude of $V_\text{max}$ as shown in the figure below. Our objective is to draw the net phasor diagram for the currents in this circuit. Also, we want to determine an expression for the net impedance in the circuit using the phasor diagram geometry.

To do this, we will use the formula for the reactance of a capacitor and an inductor:

$X_C = \frac{1}{\omega C} \tag{1}$

$X_L = \frac{1}{\omega C} \tag{2}$

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