Differential Equations d In a series circuit we have an inductor of 100 mH, a resistor...
I need help with this question of Differential Equation. Thanks In a series circuit we have an inductor of 100 mH, a resistor of 109 and a capacitor of 1000uF. At time to the capacitor carries no charge and á 90) = 0. An external voltage of E(t) = cos(100t) V is applied to the circuit. Compute the steady state charge of the capacitor. i R E(t) C L
RLC circuit in series A resistor R is connected in series to an inductor L and a capacitor C, without any external emf sources. (a) Using the fact that the energy stored in both the capacitor and the inductor is being dissipated in the resistor, show that the charge on the capacitor q(t) satisfies the differential equation d^2 q/ dt^2 + Rdq/Ldt + q/LC = 0. This is the equation of a damped oscillator and it has a solution of...
1) An (open) electrical circuit consists of an inductor, a resistor, and a capacitor. There is an initial charge of 1 coulomb on the capacitor. At the instant the circuit is closed, a current of 7 amperes is present and a voltage of E(t) = 20 cos t is applied. In this circuit the voltage drop across the resistor is 7 times the instantaneous change in the charge, the voltage drop across the capacitor is 11 times the charge, and...
A 20mH inductor, a 40.0 Ohm resistor, a 50.0 muF capacitor, and voltage source of 100 e^-100t are connected in series in an electric circuit. Find the charge on the capacitor as a function of time t, if q = 0 and i = 0 when t = 0
Exercise 31 A series ac circuit contains a 350 - resistor, a 20.0 - mH inductor, a 2.90 - uF capacitor, and an ac power source of voltage amplitude 45.0 V operating at an angular frequency of 360 rad/s. Part A What is the power factor of this circuit? ANSWER: cos - Part B Find the average power delivered to the entire circuit ANSWER: P- w Part C What is the average power delivered to the resistor, to the capacitor,...
An (open) electrical circuit consists of an inductor, a resistor, and a capacitor. There is an initial charge of 1 coulomb on the capacitor. At the instant the circuit is closed, a current of 5 amperes is present and a voltage of E(t) = 23 cost is applied. In this circuit the voltage drop across the resistor is 5 times the instantaneous change in the charge, the voltage drop across capacitor is 11 times the charge, and the voltage drop...
2-a)-RLC components connected in series in a circuit supplied by a variable dc voltage can be described by the following differential equations: di(t) wherei@ is the loop current and V1(t) İs the voltage drop across the inductor.+' The voltage drop across the resistor is given by Ohm's law vR(t) R i(t) and the voltage drop across the capacitor vc(t) is given by i(t) dt For a series circuit ye)t vit)t velt) v(t) where v(t) is applied voltage: Figure 3: RLC...
An RLC series circuit with 150-ohm resistor, 25-mH inductor, and 2 microfarad-capacitor is powered by an AC voltage source with a peak voltage of 340V and a frequency of 660 Hz. (a) Find the peak current that flows in the circuit. (b) Determine the phase angle of the source voltage relative to the current. (c) Determine the peak voltage across the resistor and its phase angle relative to the voltage source. (d) Find the peak voltage across the inductor and...
An RLC series circuit with 150-ohm resistor, 25-mH inductor, and 2 microfarad-capacitor is powered by an AC voltage source with a peak voltage of 340V and a frequency of 660 Hz. (a) Find the peak current that flows in the circuit. (b) Determine the phase angle of the source voltage relative to the current. (c) Determine the peak voltage across the resistor and its phase angle relative to the voltage source. (d) Find the peak voltage across the inductor and...
A series AC circuit contains a resistor, an inductor of 220 mH, a capacitor of 4.20 ur, 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 69.11 (b) Calculate the capacitive reactance 757.88 (c) Calculate the impedance 141 (d) Calculate the resistance in the circuit. 6.887 The impedance is a function of the resistance and the impedances of the inductor and capacitor. kΩ (e) Calculate...