Question

In: Advanced Math

Suppose an electrical circuit contains a 1 H inductor, a 10 Ω resistor and a capacitor...

Suppose an electrical circuit contains a 1 H inductor, a 10 Ω resistor and a capacitor rated at 1/7 F. If the circuit is hooked up to an alternating voltage source described by E(t) = 68 cost V and initially q(0) = 1 C and i(0) = 0 A, find a function that describes the charge as a function of time.  Lq'' + Rq' + q/C = E(t).  

Please show work using a complementary and particular solution if possible.

Solutions

Expert Solution

Colby Messinger answered 2 years ago
Next > < Previous

Related Solutions

One RL series circuit contains the resistor R1= 2 Ω and inductor L = 10 H....
One RL series circuit contains the resistor R1= 2 Ω and inductor L = 10 H. (i) Write the first order differential equation for this circuit in time constant form. (ii) Determine the time constant for this system (iii) Calculate the steady state gain of the system. (iv) Determine the time constant and steady state gain when the inductance is doubled (v) In the context of positioning of poles on the S-plane, what does the ‘real part’ represent and what...
An RLC series circuit consists of a 450-Ω resistor, a 3.00-mF capacitor, and a 1.00-H inductor....
An RLC series circuit consists of a 450-Ω resistor, a 3.00-mF capacitor, and a 1.00-H inductor. The circuit is driven by a power source that oscillates at 20.0 Hz and has an ε_rms value of 90.0 V . The power source is switched on at t = 0 and at that instant the emf is at its maximum value. A) Calculate the power supplied at t = 0.0200 s. B) Calculate the power supplied at t = 0.0375 s. C)...
An RLC series circuit consists of a 450-Ω resistor, a 3.00-mF capacitor, and a 1.00-H inductor....
An RLC series circuit consists of a 450-Ω resistor, a 3.00-mF capacitor, and a 1.00-H inductor. The circuit is driven by a power source that oscillates at 20.0 Hz and has an Erms value of 30.0 V . The power source is switched on at t = 0 and at that instant the emf is at its maximum value. Part A Calculate the power supplied at t = 0.0200 s. Part B Calculate the power supplied at t = 0.0375...
A 215 Ω resistor, a 0.900 H inductor, and a 6.50 μF capacitor are connected in...
A 215 Ω resistor, a 0.900 H inductor, and a 6.50 μF capacitor are connected in series across a voltage source that has voltage amplitude 29.5 Vand an angular frequency of 220 rad/s . a) What is v at t= 18.0 ms ? ANS: -27.7V b) What is vR at t= 18.0 ms ? c)What is vL at t= 18.0 ms ? d)What is  vC at t= 18.0 ms ? e)What is VR? f)What is VC? g)What is VL?
A 197 Ω resistor, a 0.925 H inductor, and a 5.75 μF capacitor are connected in...
A 197 Ω resistor, a 0.925 H inductor, and a 5.75 μF capacitor are connected in series across a voltage source that has voltage amplitude 31.5 V and an angular frequency of 230 rad/s. What is v at t= 19.0 ms? What is vR at t= 19.0 ms? What is vL at t= 19.0 ms? What is  vC at t= 19.0 ms? Compare vC+vL+vR and v at this instant. What is VR? What is VC? What is VL? Compare V and...
A 190 Ω resistor, a 0.875 H inductor, and a 5.75 μF capacitor are connected in...
A 190 Ω resistor, a 0.875 H inductor, and a 5.75 μF capacitor are connected in series across a voltage source that has voltage amplitude 32.0 V and an angular frequency of 270 rad/s. A. What is v at t= 22.0 ms ? B. What is vR at t= 22.0 ms ? C. What is vL at t= 22.0 ms ? D. What is vC at t= 22.0 ms ? E. Compare vC+vL+vR and v at this instant: vC+vL+vR<v vC+vL+vR>v...
A series AC circuit contains a resistor, an inductor of 240 mH, a capacitor of 5.40...
A series AC circuit contains a resistor, an inductor of 240 mH, a capacitor of 5.40 µF, and a source with ΔVmax = 240 V operating at 50.0 Hz. The maximum current in the circuit is 170 mA. (a) Calculate the inductive reactance. _________________Ω (b) Calculate the capacitive reactance. ______________-Ω (c) Calculate the impedance. _______________kΩ (d) Calculate the resistance in the circuit. ______________kΩ (e) Calculate the phase angle between the current and the source voltage. _______________°
A series ac circuit contains a 210 Ω resistor, a 20.0 mH inductor, a 3.30 μF...
A series ac circuit contains a 210 Ω resistor, a 20.0 mH inductor, a 3.30 μF capacitor, and an ac power source of voltage amplitude 45.0 V operating at an angular frequency of 360 rad/s . 1)What is the power factor of this circuit? 2)Find the average power delivered to the entire circuit. 3)What is the average power delivered to the resistor, to the capacitor, and to the inductor?
A 200 Ω resistor is in series with a 8.50×10−2 H inductor and a 0.540 μF...
A 200 Ω resistor is in series with a 8.50×10−2 H inductor and a 0.540 μF capacitor. part A: Compute the impedance of the circuit at a frequency of f1 = 500 Hz and at a frequency of f2 = 1000 Hz . Enter your answer as two numbers separated with a comma. part b: In each case, compute the phase angle of the source voltage with respect to the current. Enter your answer as two numbers separated with a...
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...
ADVERTISEMENT
Subjects
ADVERTISEMENT
Latest Questions
ADVERTISEMENT