use R=1Ω, L=1H and C= 1/5 F Instead
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use R=1Ω, L=1H and C= 1/5 F Instead (c) In the circuit shown in Figure P2.61(c),...
2. In the circuit shown in Figure 2, let C=0.5 F L=1H, R-312. Find the voltage vo(t) for t>0 L volt) Figure 2 2. In the circuit shown in Figure 2, let C=0.5 F L=1H, R-312. Find the voltage vo...
2. In the circuit shown in Figure 2, let C=0.5 F L=1H, R-312. Find the voltage vo(t) for t>0 L volt) Figure 2
2. In the circuit shown in Figure 2, let C=0.5 F L=1H, R-312. Find the voltage vo(t) for t>0 L volt) Figure 2
subject: signals and systems 2. Consider the electric circuit shown in Fig. ??, L = 1H,...
subject: signals and systems
2. Consider the electric circuit shown in Fig. ??, L = 1H, C = 1F. • Determine the differential equation that relates the input (t) to output y(t). Recall that ic(t) = C2C and vy(t) = • Find the characteristic equation for this circuit. • Determine the zero-input response given an initial capacitor voltage of one volt and an initial inductor current of zero ampere. That is, find yo(t) given uc(0) = 2V and iL(0) =...
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...
Consider the following circuit , where the voltage v(t) is imposed for t 2 0, R 4 Ω, L-1H and C 1/4F. The initial in...
Consider the following circuit , where the voltage v(t) is imposed for t 2 0, R 4 Ω, L-1H and C 1/4F. The initial initial current going through the inductor is i(0-) -0 A and its first derivative is i(0)-1A/s. We are interested in the evolution of the current i(t). ve(t) i(t) The corresponding input-output relationship is i(r)dr Ug(t) + Li'(t) + Ri(t)-r(t) with t e(t)-ve(0) + (0) Which physical quantity is the input of the system? Explain. (ü) Which...
Consider a causal LTI system implemented as the RL circuit shown below. In this circuit, v(t)...
Consider a causal LTI system implemented as the RL circuit shown below. In this circuit, v(t) is the input voltage. The current i(t) is considered the system output. i(t) R L wwwm v(t) (a) Find the differential equation relating v(t) and i(t). (b) Determine the frequency response of this system (H(jw)). (c) Determine the output it) if v(t) = sin(t), R=10 and L=1. (d) Sketch Bode plot of H (jw) for R=10 and L=1. (e) Determine if the system 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...
5. The circuit elements in the circuit in Figure 1 are R=1250, L=200mH, and C= 5uF....
5. The circuit elements in the circuit in Figure 1 are R=1250, L=200mH, and C= 5uF. The initial inductor current is -0.3A and the initial capacitor voltage is 25V. a) Calculate the initial current in each branch of the circuit. b) Find v(t) and it(t) fort > 0. + IR V. 200mH 110 12503 5uF 0 2
3. RLC Parallel Circuit a) (7pts) For the circuit shown, determine the ODE relating the voltage...
3. RLC Parallel Circuit a) (7pts) For the circuit shown, determine the ODE relating the voltage (t) to the current source is(t) as well as the > L corresponding transfer function z(s) = (Hint: It might be easier to find the latter before the former.] (12pts) For R-0.802, C=0.25F and L=1H, determine the (1) impulse response, (ii) the unit step response and (111) the response to a pure sinusoid is (t) = cos(itt) Amperes (note that this last function is...
As shown in the figure, a simple RL circuit (L = 1H) is powered by a...
As shown in the figure, a simple RL circuit (L = 1H) is powered by a 10 V batterey. The initial current in the circuit is zero. (el-0.367 -0.135, -0.049, e---0.018, e'-0.006) R t-0)0 time (sec) Vc (Volt) MW 6.33 8.65 9.51 9.82 9.94 3 4 5 6 7 8 sec.) a) Calculate the time constant of the RL circuit using the graph given above. O b) Calculate VR(t) the voltage across the resistor R. as a function of time....
Am (t) → volt) Figure Q1 R = 10, L = H, C = F Q1(a)...
Am (t) → volt) Figure Q1 R = 10, L = H, C = F Q1(a) [2 marks] The transfer function for the circuit in Figure V.(s)__ LC Vin(5) sz+s+ + Form the corresponding differential equation that governs the behaviour of the system Q1(b) [4 marks] Determine a state-space representation for the circuit in Figure Q1 with the states selected as x;(6) v.) and x2(t) = 1,t). Show that it is equal to the following 408 J18+) y(t) = [1...
2. In the circuit shown in Figure 2, let C=0.5 F L=1H, R-312. Find the voltage vo(t) for t>0 L volt) Figure 2
2. In the circuit shown in Figure 2, let C=0.5 F L=1H, R-312. Find the voltage vo(t) for t>0 L volt) Figure 2
subject: signals and systems
2. Consider the electric circuit shown in Fig. ??, L = 1H, C = 1F. • Determine the differential equation that relates the input (t) to output y(t). Recall that ic(t) = C2C and vy(t) = • Find the characteristic equation for this circuit. • Determine the zero-input response given an initial capacitor voltage of one volt and an initial inductor current of zero ampere. That is, find yo(t) given uc(0) = 2V and iL(0) =...
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...
Consider the following circuit , where the voltage v(t) is imposed for t 2 0, R 4 Ω, L-1H and C 1/4F. The initial initial current going through the inductor is i(0-) -0 A and its first derivative is i(0)-1A/s. We are interested in the evolution of the current i(t). ve(t) i(t) The corresponding input-output relationship is i(r)dr Ug(t) + Li'(t) + Ri(t)-r(t) with t e(t)-ve(0) + (0) Which physical quantity is the input of the system? Explain. (ü) Which...
Consider a causal LTI system implemented as the RL circuit shown below. In this circuit, v(t) is the input voltage. The current i(t) is considered the system output. i(t) R L wwwm v(t) (a) Find the differential equation relating v(t) and i(t). (b) Determine the frequency response of this system (H(jw)). (c) Determine the output it) if v(t) = sin(t), R=10 and L=1. (d) Sketch Bode plot of H (jw) for R=10 and L=1. (e) Determine if the system is...
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...
5. The circuit elements in the circuit in Figure 1 are R=1250, L=200mH, and C= 5uF. The initial inductor current is -0.3A and the initial capacitor voltage is 25V. a) Calculate the initial current in each branch of the circuit. b) Find v(t) and it(t) fort > 0. + IR V. 200mH 110 12503 5uF 0 2
3. RLC Parallel Circuit a) (7pts) For the circuit shown, determine the ODE relating the voltage (t) to the current source is(t) as well as the > L corresponding transfer function z(s) = (Hint: It might be easier to find the latter before the former.] (12pts) For R-0.802, C=0.25F and L=1H, determine the (1) impulse response, (ii) the unit step response and (111) the response to a pure sinusoid is (t) = cos(itt) Amperes (note that this last function is...
As shown in the figure, a simple RL circuit (L = 1H) is powered by a 10 V batterey. The initial current in the circuit is zero. (el-0.367 -0.135, -0.049, e---0.018, e'-0.006) R t-0)0 time (sec) Vc (Volt) MW 6.33 8.65 9.51 9.82 9.94 3 4 5 6 7 8 sec.) a) Calculate the time constant of the RL circuit using the graph given above. O b) Calculate VR(t) the voltage across the resistor R. as a function of time....
Am (t) → volt) Figure Q1 R = 10, L = H, C = F Q1(a) [2 marks] The transfer function for the circuit in Figure V.(s)__ LC Vin(5) sz+s+ + Form the corresponding differential equation that governs the behaviour of the system Q1(b) [4 marks] Determine a state-space representation for the circuit in Figure Q1 with the states selected as x;(6) v.) and x2(t) = 1,t). Show that it is equal to the following 408 J18+) y(t) = [1...
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