Suppose that an inductor (L) - resistor (R) – capacitor (C) circuit is connected to an AC source that has a frequency of n rad/s. An engineer measured the values: the resistor's resistance which was found to be 10 ohms, the inductor's inductance was found to be 10 H, while the capacitor's capacitance was found to be 10 F. Determine the value of impedance. а. 10 ohms b. 33 ohms с. 11.5 ohms d. 1,080 ohms
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- A resistance R, capacitance C, and inductance L are connected in series to a voltage source with amplitude V and variable angular frequency v. If w = w0 , the resonance angular frequency, find (a) the maximum current in the resistor; (b) the maximum voltage across the capacitor; (c) the maximum voltage across the inductor; (d) the maximum energy stored in the capacitor; (e) the maximum energy stored in the inductor. Give your answers in terms of R, C, L, and V.Cell phones that use 4G technology receive signals broadcast between 2 GHz and 8 GHz. (a) If you want to create a simple L-R-C series circuit to detect a 4.0 GHz cell phone signal, what is the relevant value of the product LC, where L is the inductance and C is the capacitance? (b) If you choose a capacitor that has C = 1.0 * 10-15 F, what inductance do you need? (c) Suppose you want to wind your own toroidal inductor and fit it inside a box as thin as your cell phone. Based on the size of your phone, estimate the largest cross-sectional area possible for this. (d) Assume the largest allowable radius of the toroid is 1.0 cm and estimate the lowest number of windings needed to create your inductor, assuming the material inside has a relative permeability of 1.A circuit is designed with an AC source of max voltage 12 and frequency 60 Hz. The circuit has a resistance of 1050 Ohms, an inductance of 0.06 Henrys, and a capacitance of 0.009 coulombs per volt. - omega for source in rad/s? - omegaR for circuit? -XL? -XC? -phi in radians? -Z? -imax?
- Solve for the total capacitance from the circuit shownA voltage vC(t)=10 cos(2000πt) is applied to a 10-μF capacitance. Find the complex impedance of the capacitance. Find the phasor voltage and current, and construct a phasor diagram. Write the current as a function of time. Sketch the voltage and current to scale versus time. State the phase relationship between the current and voltage.A resistor, an inductor, and a capacitor are connected in parallel to an ac source with voltage amplitude V and angular frequency v. Let the source voltage be given by v = Vcosvt. (a) Show that each of the instantaneous voltages vR, vL, and vC at any instant is equal to v and that i = iR + iL + iC, where i is the current through the source and iR, iL, and iC are the currents through the resistor, inductor, and capacitor, respectively. (b) What are the phases of iR, iL, and iC with respect to v? Use current phasors to represent i, iR, iL, and iC. In a phasor diagram, show the phases of these four currents with respect to v. (c) Use the phasor diagram of part (b) to show that the current amplitude I for the current i through the source is I = √(I2R) + (IC - IL)2 . (d) Show that the result of part (c) can be written as I = V/Z, with 1/Z = √ (1/R2) + [ωC - (1/ωL)]2.
- A capacitor with capacitance C is connected to an AC source. If the AC source provides a voltage VC(t) = V0cos(omegat), what is the current IC(t) through the capacitor as a function of time? Use the cosine function.A LC circuit in a radio tuned to 1080 kHz has an inductor with an inductance value of 60 μH and a resistance of 0.25 Ω. a. what is the capacitance of the LC circuit? b. sketch the impedance phasor diagram for the radio. Be sure to label important features of the diagram.A 20µF capacitor has a sinusoidal voltage across it given by?(?) = 5 sin(500? + 45°) V.(a) Find the phasor representation of the voltage in polar (magnitude and phase) form.(b) Find the phasor representation of the voltage in Cartesian (real and imaginary part) form.(c) Find the phasor representation of the current through the capacitor. (d) If this same voltage appeared across the terminals of a 100mH inductor, what would be thephasor representation of the inductor current?
- What is incorrect about the RLC AC Circuit shown? 1 The power dissipation through the (ideal) capacitor is vanishing. 2 The current leads the voltage across the capacitor by 90deg. 3 The voltage across the inductor leads the current by 90deg. 4 If the AC source is replaced by a constant DC source, after a very longtime, the voltage across the inductor vanishes. 5 If the AC source is replaced by a constant DC source, after a very longtime, the voltage across the capacitor will be equal to that across theresistor.The current through a 100-mH inductance is given by i( t )=exp( −t ) sin( 10t ) in which the angle is in radians. Determine the voltage across the inductance. Then, use the computer program of your choice to plot both the current and the voltage for 0≤t≤3 s.a) What is the time domain expression for the current? b) If the load impendance is created by an inductor with value L=375 mH, find the phaser voltage Vx? c) If the load impendance is created by a capacitor with value C=16.7 uF, find the phaser voltage Vx?