It shows that the electric circuit shown in the figure
is described by the system of differential equations. Where x1 is
the current that will pass through the coil, x2 is the voltage drop
in the capacitor, and I (t) is the current produced by the external
source
Explain your procedure
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It shows that the electric circuit shown in the figure is described by the system of differential equations. Where x1 is...
R wW L Consider the electric circuit in the figure above. This circuit is described by...
R wW L Consider the electric circuit in the figure above. This circuit is described by the system of differential equations d dt RC Suppose that R = 1 ohms, C= 5 farads, and L 20 henrys. Suppose also that i (0) 2 amperes and v (0) 36 volts. Find i (t) and v (t). Click here to enter or edit your answer i(t) The solution is given by v(t) Click if vou would like to Show Work for this...
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 vol...
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...
TASK (i): Find time-domain equations for a parallel LC resonant circuit An LC resonant circuit is...
TASK (i): Find time-domain equations for a parallel LC resonant circuit An LC resonant circuit is sometimes referred to as an LC-tank or tuned circuit. It is made up of two components: an inductor (L) and a capacitor (C), hence the name. CAPACITOR 4 e V - + V - Figure 1: Capacitor symbol The charge on a capacitor is proportional to the voltage across it, the constant of proportionality being the capacitance C, measured in Farads (F). Since current...
The circuit in the figure to the right is represented by the equation below, where I...
The circuit in the figure to the right is represented by the equation below, where I is the current through the inductor Land Ve is the voltage drop across the capacitor C. Find formulas for I, and Vc when R=0.5 ohms, C = 12.5 farads, L= 2.5 henry, the initial current is o amperes, and the initial voltage is 12 volts. R Het с 1 RC Vc 000 L Choose the correct answer below. 4.(t) Vc(t) 0.100 OA 30 sin(-0.08t)...
8 -12 a. Find the most general real-valued solution to the linear system of differential equations...
8 -12 a. Find the most general real-valued solution to the linear system of differential equations zē' = [; . 9-13 x1(t) = = C1 + C2 X2(t) - b. In the phase plane, this system is best described as a source / unstable node sink / stable node saddle O center point / ellipses spiral source Ospiral sink none of these
Differential Equations d In a series circuit we have an inductor of 100 mH, a resistor...
Differential Equations
d In a series circuit we have an inductor of 100 mH, a resistor of 1012 and a capacitor of 1000uF. At time t=0 the capacitor carries no charge and 9(0) = 0. An external voltage of E(t) = cos(100t) V is applied to the circuit. Compute the steady state charge of the capacitor. dt R E(t) = HE L
Linear Algebra and differential Equations. Consider the RLC circuit with R = 180Ω, C = 1/280F,...
Linear Algebra and
differential Equations.
Consider the RLC circuit with R = 180Ω, C = 1/280F, L = 20H, and applied voltage E(t) = 10 sin t. Assuming no initial charge on the capacitor, but an initial current of 1 ampere. Determine the charge on the capacitor for t> 0. (a) Write the differential equation, y', +4xy'-6x2y = x2 sin x, as an operator equation and give the associated homogeneous DE (b) Write the DE (D2 1) (D 3)(y) e...
L c The amounts x1 (t) and x2 (t) of salt in two brine tanks satisfy the differential equations b...
l c The amounts x1 (t) and x2 (t) of salt in two brine tanks satisfy the differential equations below where ki = for i= 1. 2. The volumes are V,-50 (gal) and v2-25 (gal). First solve for x1(t) and x2(t) assuming that r#20 (gai in). x1(0): 25(b), and x2(0)-Ο Then find the maximum amount of salt ever in tank 2 Finally, construct a figure showing the graphs of x,(t) and x2t) dx1 dx2
l c The amounts x1 (t)...
Chapter 7, Section 7.5, Question 32a An electric circuit is described by the system of differential...
Chapter 7, Section 7.5, Question 32a An electric circuit is described by the system of differential equations (0) - -1 CR (). lu Find the general solution of this equation if R1 - 1 ohm, R2 = 39 ohm, L = 6 henrys, and 6 35 farad. -60 1 -35 e to @=c(1) +c2 ()--(-2)***+52 cal (=cz(1) ++ 1 -35 1 -6t +cz le 35 6t (0) --()e# 1 e3' + C2 35 ID 6t ( )=(-)}'+62 1 -35 le
Find the most general real-valued solution to the linear system of differential equations (1 point) a. Find the most gen...
Find the most general real-valued solution to the linear system
of differential equations
(1 point) a. Find the most general real-valued solution to the linear system of differential -5 -36 x. -5 equations x 1 CHH x1 (t) = C1 x2 (t) b. In the phase plane, this system is best described as a O source/ unstable node Osink /stable node Osaddle center point ellipses Ospiral source spiral sink none of these tsi O O O
(1 point) a. Find...
R wW L Consider the electric circuit in the figure above. This circuit is described by the system of differential equations d dt RC Suppose that R = 1 ohms, C= 5 farads, and L 20 henrys. Suppose also that i (0) 2 amperes and v (0) 36 volts. Find i (t) and v (t). Click here to enter or edit your answer i(t) The solution is given by v(t) Click if vou would like to Show Work for this...
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...
TASK (i): Find time-domain equations for a parallel LC resonant circuit An LC resonant circuit is sometimes referred to as an LC-tank or tuned circuit. It is made up of two components: an inductor (L) and a capacitor (C), hence the name. CAPACITOR 4 e V - + V - Figure 1: Capacitor symbol The charge on a capacitor is proportional to the voltage across it, the constant of proportionality being the capacitance C, measured in Farads (F). Since current...
The circuit in the figure to the right is represented by the equation below, where I is the current through the inductor Land Ve is the voltage drop across the capacitor C. Find formulas for I, and Vc when R=0.5 ohms, C = 12.5 farads, L= 2.5 henry, the initial current is o amperes, and the initial voltage is 12 volts. R Het с 1 RC Vc 000 L Choose the correct answer below. 4.(t) Vc(t) 0.100 OA 30 sin(-0.08t)...
8 -12 a. Find the most general real-valued solution to the linear system of differential equations zē' = [; . 9-13 x1(t) = = C1 + C2 X2(t) - b. In the phase plane, this system is best described as a source / unstable node sink / stable node saddle O center point / ellipses spiral source Ospiral sink none of these
Differential Equations
d In a series circuit we have an inductor of 100 mH, a resistor of 1012 and a capacitor of 1000uF. At time t=0 the capacitor carries no charge and 9(0) = 0. An external voltage of E(t) = cos(100t) V is applied to the circuit. Compute the steady state charge of the capacitor. dt R E(t) = HE L
Linear Algebra and
differential Equations.
Consider the RLC circuit with R = 180Ω, C = 1/280F, L = 20H, and applied voltage E(t) = 10 sin t. Assuming no initial charge on the capacitor, but an initial current of 1 ampere. Determine the charge on the capacitor for t> 0. (a) Write the differential equation, y', +4xy'-6x2y = x2 sin x, as an operator equation and give the associated homogeneous DE (b) Write the DE (D2 1) (D 3)(y) e...
l c The amounts x1 (t) and x2 (t) of salt in two brine tanks satisfy the differential equations below where ki = for i= 1. 2. The volumes are V,-50 (gal) and v2-25 (gal). First solve for x1(t) and x2(t) assuming that r#20 (gai in). x1(0): 25(b), and x2(0)-Ο Then find the maximum amount of salt ever in tank 2 Finally, construct a figure showing the graphs of x,(t) and x2t) dx1 dx2
l c The amounts x1 (t)...
Chapter 7, Section 7.5, Question 32a An electric circuit is described by the system of differential equations (0) - -1 CR (). lu Find the general solution of this equation if R1 - 1 ohm, R2 = 39 ohm, L = 6 henrys, and 6 35 farad. -60 1 -35 e to @=c(1) +c2 ()--(-2)***+52 cal (=cz(1) ++ 1 -35 1 -6t +cz le 35 6t (0) --()e# 1 e3' + C2 35 ID 6t ( )=(-)}'+62 1 -35 le
Find the most general real-valued solution to the linear system
of differential equations
(1 point) a. Find the most general real-valued solution to the linear system of differential -5 -36 x. -5 equations x 1 CHH x1 (t) = C1 x2 (t) b. In the phase plane, this system is best described as a O source/ unstable node Osink /stable node Osaddle center point ellipses Ospiral source spiral sink none of these tsi O O O
(1 point) a. Find...
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