Question

In: Physics

A circuit is consisted of an inductor L, a capacitor C, and a resistor R. It...

A circuit is consisted of an inductor L, a capacitor C, and a resistor R. It is driven by an AC voltage of the form ?0sin (??). At the steady state, find (a) the charge and current as a function of time (b) the maximum amplitude of the current and the corresponding resonance frequency (c) the average power at the current’s resonance frequency (c) the quality factor Q

Solutions

Expert Solution

The answer are on the images. Page number is mentioned at right top.


Related Solutions

In the given circuit an inductor of L = 8.95-mH and a resistor of R =...
In the given circuit an inductor of L = 8.95-mH and a resistor of R = 17.9-Ω resistor are connected in series with a dc battery of E = 8.80-V. What is the voltage across the resistor immediately after the switch is closed? What is the voltage across the resistor after the switch has been closed for a long time? What is the current in the inductor after the switch has been closed for a long time?
1. An L-R-C circuit consists of a 5 µF capacitor, a 2 mH inductor and a...
1. An L-R-C circuit consists of a 5 µF capacitor, a 2 mH inductor and a 50 Ω resistor, connected in series to an ac source of variable angular frequency ω, but of fixed voltage amplitude V​​​​​​s. At the resonance frequency, the amplitude of the current oscillations in this circuit is measured to be 100 mA. (a) In your own words explain what is meant by the resonance behaviour of an L-R-C series ac circuit. At what frequency of the...
An L-R-C series circuit consists of a 2.40 μF capacitor, a 6.00 mH inductor, and a...
An L-R-C series circuit consists of a 2.40 μF capacitor, a 6.00 mH inductor, and a 60.0 Ω resistor connected across an ac source of voltage amplitude 10.0 V having variable frequency. Part A: At what frequency is the average power delivered to the circuit equal to 1/2*V_rms*I_rms? (ω = ____rad/s) Part B: Under the conditions of part (a), what is the average power delivered to each circuit element? (P_R, P_C, P_L = ____W) Part C: What is the maximum...
A circuit is constructed with an AC generator, a resistor, capacitor and inductor as shown. The...
A circuit is constructed with an AC generator, a resistor, capacitor and inductor as shown. The generator voltage varies in time as ε =Va - Vb = εmsinωt, where εm = 120 V and ω = 231 radians/second. The inductance L = 155 mH. The values for the capacitance C and the resistance R are unkown. What is known is that the current in the circuit leads the voltage across the generator by φ = 49 degrees and the average...
An L-R-C series circuit consists of a 60.0 Ω resistor, a 10.0 μF capacitor, a 3.60...
An L-R-C series circuit consists of a 60.0 Ω resistor, a 10.0 μF capacitor, a 3.60 mH inductor, and an ac voltage source of voltage amplitude 60.0 V operating at 1450 Hz . a.) Find the current amplitude across the inductor, the resistor, and the capacitor. b.) Find the voltage amplitudes across the inductor, the resistor, and the capacitor. c.) Why can the voltage amplitudes add up to more than 60.0 V ? d.) If the frequency is now doubled,...
An RLC circuit is made up of a resistor R = 12Ω , a capacitor C...
An RLC circuit is made up of a resistor R = 12Ω , a capacitor C = 0.1 F and an inductor L = 2 H. A voltage source is connected that supplies 110 V. If initially the capacitor is discharged and no current flows through the circuit, find an expression for the charge at all times t. differential equations
Consider a circuit that consists of a resistor with R = 40Ω, and an inductor with...
Consider a circuit that consists of a resistor with R = 40Ω, and an inductor with L = 1H, a capacitor with C = 0.002F, and a 15V battery. 1. Write the differential equation for the charge Q 2. Classify the equation (order, linear/non-linear, homogeneous/nonhomogeneous) 3. Find two solutions of the complementary equation and show that they form a fundamental set of solutions. 4. Find the general solution of the equation. 5. Assume that the initial charge and current are...
a circuit that has a resistor, capacitor, and inductor in series with a 5V AC voltage...
a circuit that has a resistor, capacitor, and inductor in series with a 5V AC voltage source R = 5 Ω; L = 1 mH; C = 447 a) Find ω0 and f0 b) Complete the table f = f0 f = 0.5f0 f = 1.5f0 I VL Vc c) What is the phase between circuit current and applied voltage at f = f0 (in radians) d) Determine if the below statements are true or false Below resonance (f <...
An RLC circuit consists of a resistor R = 12 LaTeX: \ OmegaΩ, a capacitor C...
An RLC circuit consists of a resistor R = 12 LaTeX: \ OmegaΩ, a capacitor C = 0.1 F and an inductor L = 2 H. A voltage source is connected that supplies 110 V. If initially the capacitor is discharged and no current flows through the circuit, find an expression for the charge at all times t.
Driven RC circuit in parallel. A capacitor C is connected in parallel to a resistor R...
Driven RC circuit in parallel. A capacitor C is connected in parallel to a resistor R and an AC source providing a voltage v(t) = V sin(ωt). (a) Make a phasor diagram at time t showing all relevant based on Kirchhoff’s rules. (b) Find the impedance of this circuit and make a plot of Z vs. ω. (c) What are the small and large frequency behaviors of the peak capacitor and resistor currents? (d) What is the phase difference between...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT