Consider the RC circuit shown in figure. Find the following: (a) The governing differential equation for the system where vo(t) is output and v.(t) is input. (b) The transfer function for the circuit + Vs C₁ www R₁ R2 WI C₂ = Vo
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- In an RC circuit, what is the value of the ratio V. /E when the current in the circuit reaches 13.95% of its peak value? V. = voltage across the capacitor and E = emf of the %3D power source. Express your result as a percentage with 2 decimal places (i.e if the result is 76.14 % write 76.14 without the % sign and not 0.7614)An RC circuit has an emf of 10 sin t (volts), a resistance of 100 ohms, a capacitance of 0.005 farad, and no initial charge on the capacitor. (a)what is the differential equation governing the amount of charge on the capacitor? (b) what is the integrating factor of it?(c) what is the charge on the capacitor at any time t? (d)what is the current in the circuit at any time t?An RC circuit will have an exponential voltage response of the form v(t) = A+Be^(-t/RC) where A and B are constants that express the final voltage and the difference between the initial voltage and the final voltage, respectively. a) Given: R = 10 k2 and C = 0.1 µF, a starting voltage of 5 Volts and an ending voltage of 0 Volts, what will the voltage be at t= 1 ms? b) At what time will the voltage be 0.5 Volts?
- Consider the series RC-circuit shown below for which R = 40.0 k2, C = 35.0 µF, and E = 27.0 V. Find the following. 0.632cE 7-RC R (a) (b) (a) the time constant of the circuit (b) the charge on the capacitor one time constant after the switch is closedConsider an electric circuit containing a capacitor, resistor, and battery; see the figure. The charge Q(t) on the capacitor satisfies the R V equation R dt O' OP V, where R is the C resistance, C is the capacitance, and V is the constant voltage supplied by the battery. a) If Q(0) = 0, find Q(t) at any time t, and sketch the graph of Q versus t. Q(t) = %3D b) Find the limiting value QL that Q(t) approaches after a long time. The limiting value Qz that Q(t) approaches after a long time is QL c) Suppose that Q(tı) = QL and that at time t = t; the battery is removed and the circuit is closed again. Find Q(t) for t > tį and sketch its graph. Q(t) =Consider the circuit shown below. If the voltage source is set to 10 V, R1 = 800 and R3 = 800. Choose R2 so that the current through that resistor is equal to 10 mA. Compute the total power dissipated by the circuit.
- Context: Source of EMF and RC Circuits How do you derive Equation 4 from Equations 1 and 3? Equation 1 is Current, I= emf/(R+r) and Equation 3 is power, P= IV= I^2R . Equation 4 is Making use of Eq. (1) in Eq. (3), one can show that power, P, supplied by the battery to the resistive load, R, can be written as: P=emf^2(R/(R+r)^2An electrical circuit that includes a voltage source 8. vs with an internal resistance rs and a load resis- tance R, is shown in the figure. The power P dissi- rsi Battery pated in the load is given by vR, P = (RL +rs) RL ww Plot the power P as a function of R for I RS 102, given that vs = 12 V and rs = 2.5 2.A series RC circuit is constructed with a resistor with resistance R=260 ohms and a capacitor with capacitance C=42 uF. The circuit is initially fully charged to a maximum voltage V0=8.0V. The circuit is then discharged. (a) What are the time constant and half time of this circuit? (b) What is the voltage across the capacitor after one, two, and three half times? Remember, the circuit is discharging.
- In a simple RC circuit design, a resistor (1 MQ) and a capacitor (2 µF) are connected in series with a switch and a power supply of 20V as shown below. 3 of 7 AVT (a) (b) Figure 1: A simple RC circuit Determine the time constant (to), amount of time required for the charge on a charging capacitor to rise to 63% of its final value, of the RC-circuit and verify that (to) is consistent with your result. What is the maximum voltage and current that can be achieved at the steady state condition of the capacitor. Write down the specific time-dependent expressions for the relative charge (Q/Q.) development in the capacitor, the relative current flow (I/I,) and the relative potential difference (V/V) measured across the resistor (R) during the charging and discharging processes respectively. Sketch 3 separate graphs for the time development of the charge (Q) on the capacitor, current (I) and potential difference (V) across the resistor during the harging and discharging process in the series…Calculate the Voltage across the capacitor at time constant 1+(Tau) for the following RC Circuit. Assume switch is closed and capacitor is in a charge state. t=0 LE =10 V Vc(t) = Vo(1 - e-t/t) of R1 1kQ C1 1uFConsider the RC circuit shown in the figure below. If the resistance of the circuit is R=4kN and the capacitance of the initially uncharged capacitor is C=11µF. If emf of the battery the circuit is connected to is E=17V and the switch is closed at t=0, determine how long it would take for the capacitor to reach 86% of its maximum charge. Express your answer in units of ms (milliseconds) using one decimal place. + S