Q.5: Consider the first-order circuit with the input voltage v = 4u(t) V and v(0) = 1 V in Fig. Q5. (i) Derive the first-order differential equation with the capacitor voltage v(t) as the variable; (ii) Find the current io and the output voltage vo(t). Vs 20 ΚΩ 10 kQ2 ww 2 μF HH + v Figure Q5 I %
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Q.5: Consider the first-order circuit with the input voltage v_s = 4u(t) V and v(0) = 1 V in Fig. Q5. (i) Derive the first-order differential equation with the capacitor voltage v(t) as the variable; (ii) Find the current i_0 and the output voltage v_0(t).
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- 5. An electric circuit contains a resistance R and a capacitor C in series, and a battery supplying a time-varying electromotive force (or voltage) V(t). The charge q on the capacitor therefore obeys the following differential equation: Rdq + 2 = V(t). dt Assuming that initially there is no charge on the capacitor, and given that V(t) Vosinut, where V₂ and w are some constants, find the charge on the capacitor as a function of time. = Hint: You may have to do integration by parts twice to evaluate the following inte- gral: feRc sin(wt)dt.b. A capacitor in a RC circuit is charged for a long time as shown in the Figure below, where the battery voltage V=6V. The switch s is flipped from a to b and the capacitor discharges through the R = 4 MQ resistor. 4 seconds after the switch is flipped to discharge the capacitor, the voltage across the capacitor is 3 V. What are (a) The time constant of this circuit (b) The capacitance of the capacitor (c) The current in the circuit and the charge on the capacitor just before the switch is flipped from a to b. (d) The current in the circuit immediately after the switch is flipped from a to bApply Kirchoff's law to the circuit and write down the linearly independent voltage equations. You must draw the diagram and show the direction of currents in each of the components. The emf's in the circuit have the values E1=4V and E2=12V. The resistors have the following value of resistances R1=2.2Ω, R2=22Ω, R3=4.4Ω, and R4=3.3Ω. b) Find the current through the resistance R3. c) Find the magnitude of potential difference across the points p and q (i.e. potential difference of point q relative to point p. ).
- 15V a. + AM 10.2. 4 t=0 um 45² 652 im + V 1 ic (t) b. Assume switch has been closed for Find a mathematical expression for Vc it capacitor is initially uncharged and the switch is closed at t = 0. Sketch Vc lt). 20m F a long time. opening Fird an expression for ic immediately after the switch and sketch it.For the circuit shown in Fig. Q1(a), the capacitor is initially charged to 3.5 V with polarity shown. compute the time constant, T of the circuit. I = 5.5 mA ↑ R₁ R₂ 2.6 ΚΩ 18.7 ΚΩ Fig. Ql(a) S C = 3.3 uF + 3.5 V4. You can easily find the time constant if you are given a graph of voltage across a discharging capacitor as a function of time. When t = Tc = RC, the voltage across the capacitor is AV (t = Tc) = AV, e¹≈ 0.37 AV Therefore the time constant is just how long it takes for AV (t) to reach 37% of its initial value. The graph shows the voltage across a discharging 0.2 μF capacitor as a function of time. Use the following steps to determine the resistance. a. What is 37% of the initial voltage? 21 b. How long does it take (after discharge starts) for the voltage to reach 37% of the initial voltage? This time is equal to the time constant. c. Use your time constant from (b) to determine the resistance. AV (Volts) 2 1.5 0.5 %40 80 120 160 time (milli-sec)
- Q.4: answer one of the following A) Use mesh current method for the circuit in fig. 5, to Calculate the current in each branch B) For the: For the capacitors circuit shown in fig.6 find the Qr, Cr, and the total energy Wr . 20 Ω C1=3 µF 30 Q C2=1 µF 40 Ω C3=5 µF 60 2 50 2 10 2 20 V 100 V 50 V VT = 200V fig. 5 fig. 6A 6.00 μF capacitor that is initially uncharged is connected in series with a 4600 resistor and a 507 V emf source with negligible internal resistance. Part A Just after the circuit is completed, what is the voltage drop across the capacitor? Express your answer in volts. 195| ΑΣΦ Vc = Submit Part B VR = Submit Just after the circuit is completed, what is the voltage drop across the resistor? Express your answer in volts. Part C Request Answer 20 = Submit VO ΑΣΦ | Request Answer V ? Just after the circuit is completed, what is the charge on the capacitor? Express your answer in coulombs. ΑΣΦ Request Answer ? V ? V C Review | ConstantsThe Q vs t graph shown below is for the capacitor of an RC circuit. Q (C) 8 6. 4. 2. O 6. t(s) 10 20 30 40 50 60 70 80 90 100 4. Second graph The Q vs t graph shown below is for the capacitor of an RC circuit. Q (C) 8 2 2 3 4 Determine the time constant of the RC circuit. t(s) T= If C = 4 F, determine R. R = Ω In this case, was the capacitor charging or discharging? --Select- Determine the time constant of the RC circuit. T= If R = 102, determine C. C = In this case, was the capacitor charging or discharging? -Select- + #
- C) A 150 resistor, in series, with a capacitor of capacitance (C) is connected with an output voltage source 120 V and 4 A current passes through the circuit. Calculate phase difference (4) between voltage and current. (5 Marks) R=150 120vanswer a and b only..a12Problem 5: A current of I- 2.6 A passes through the circuit shown, where R- 65 3R 5R V) 2R 6R 2R 7R 5R 10R Otheexpertta.com Part (a) In terms of R, I, and numeric values, write an expression for the voltage of the · source, V. Part (b) What is the voltage, V in volts? tan( sin() cotanO a acos cosh0t cosO asin() acotan 4 5 6 sinh() cotanhO *1 23 0 tanh0c O Degrees O Radians CLEAR BACKSPACE