Solution Found!
(a) Sketch the phasor diagramfor an ac circuit with a
Chapter 24, Problem 24P(choose chapter or problem)
(a) Sketch the phasor diagramfor an ac circuit with a \(105-\Omega\) resistor in series with a \(32.2-\mu \mathrm{F}\) capacitor. The frequency of the generator is 60.0 Hz. (b) If the rms voltage of the generator is 120 V, what is the average power consumed by the circuit?
Questions & Answers
QUESTION:
(a) Sketch the phasor diagramfor an ac circuit with a \(105-\Omega\) resistor in series with a \(32.2-\mu \mathrm{F}\) capacitor. The frequency of the generator is 60.0 Hz. (b) If the rms voltage of the generator is 120 V, what is the average power consumed by the circuit?
ANSWER:Step 1 of 7
Given data:
The resistance of the resistor is given as \(R = 105\;\Omega\).
The capacitance of the capacitor is given as, \(C = 32.2 \times {10^{ - 6}}\;{\rm{F}}\).
The frequency of the generator is \(f = 60.0\;{\rm{Hz}}\).
To construct the phasor diagram, we start by drawing the current phasor with a Length \({I_{\max }}\) at the angle \(\theta = \omega t\) with the X-axis.
After drawing the current phasor with a length \({I_{\max }}\) at the angle \(\theta = \omega t\), draw the voltage phasor associated with the resistor. This has a magnitude \({V_{\max ,R}} = {I_{\max }}R\) and points in the same direction as the current phasor.
After this, draw the voltage phasor for the capacitor having magnitude \({V_{\max ,C}} = {I_{\max }}{X_C}\). This points in a direction 90 degrees clockwise from the voltage phasor for the resistance because voltage lags behind current by 90 degrees.
Now, to obtain the total voltage in the circuit in terms of the individual voltages, perform the vector sum of \({V_{\max ,R}}\) and \({V_{\max ,C}}\).
Step 2 of 7
This voltage is the hypotenuse of the right triangle formed by these two phasor.
Its magnitude is given by,
\({V_{\max }} = {