![[6] (10 points) n the circuit below, the resistance value of the resistor is a random variable such that R N(1,0.5). Determine and expression for the expected value of the voltage u (Note, solve the differential equation for the current and thus voltage, and then apply the solution presented in class for the expected value of an exponential function of a random variable.). i(t) 4 10u(t) V 1 H](http://img.homeworklib.com/questions/77be31a0-1acc-11ec-b6f4-6568a1edbad4.png?x-oss-process=image/resize,w_560)
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[6] (10 points) n the circuit below, the resistance value of the resistor is a random...
7 A circuit consists of a resistor of resistance R, and a capacitor of capacitance C,...
7 A circuit consists of a resistor of resistance R, and a capacitor of capacitance C, connected in series, and is described by the first order differential equation - + y = E where E is the constant e.m.f. and v is the voltage across the capacitor. Given that v(O) = 0, show by using the integrating factor method that v = E(1 - e-t/(RC))
uestion 3: (10 points) n the RC circuit in the figure, Ri = 10 KQ, R2...
uestion 3: (10 points) n the RC circuit in the figure, Ri = 10 KQ, R2 = 30 KO, and C 6 uF. aswer the following questions, ) What is the equivalent resistor R12 to R and R2? 2) Find the differential equation relating the output voltage Vout to the input voltage 3) What is the order of the system? 4) What is the time constant t? 5) For step input Vin = 10V, find an expression for the output...
If I is the current in the external resistor R and r is the internal resistance...
If I is the current in the external resistor R and r is the internal resistance of the cell, the equation for the whole circuit is: E = I(R + r) …….(i) For the same current in the external resistor R, the terminal voltage is given by: V = IR …….(ii) Use equations (i) and (ii) to solve for r by eliminating I and write this equation the form: y = mx + b Identify...
A capacitor with capacitance C is initially charged with charge q0. At time t = 0 a resistor with resistance R is connected across the capacitor. (Figure 1)
To understand the behavior of the current and voltage in a simple R-C circuit. A capacitor with capacitance C is initially charged with charge q0. At time t = 0 a resistor with resistance R is connected across the capacitor. (Figure 1) Part CNow solve the differential equation V(t) = -CR dV(t)/dt for the initial conditions given in the problem introduction to find the voltage as a function of time for any time t.
If I is the current in the external resistor R and r is the internal resistance...
If I is the current in the external resistor R and r is the internal resistance of the cell, the equation for the whole circuit is: E = I(R + r) …….(i) For the same current in the external resistor R, the terminal voltage is given by: V = IR …….(ii) Use equations (i) and (ii) to solve for r by eliminating I and write this equation the form: y = mx + b Identify...
04) The RC Circuit shown below includes both a fixed resistor and a potentiometer. By turning...
04) The RC Circuit shown below includes both a fixed resistor and a potentiometer. By turning the knob on the potentiometer, the resistance between the fixed resistor and the capacitor can be changed within the range of 0 to 20 ko. a. Is this a lowpass or high pass configuration? R = 10 kn Rror = 20 k2 C = 10 uF b. Find an expression for the voltage across the capacitor Vou(t) to a unit voltage step (the voltage...
The circuit below can be used to simulate/measure the equivalent resistance of a circuit. The voltage...
The circuit below can be used to simulate/measure the equivalent resistance of a circuit. The voltage from V, to ground will be the equivalent resistance because V-IR and in this case the current source ll is equal to 1 Amp. Note that in general Amp.s not used by a resistance meter as it can cause a too much power to be dissipated by the resistor which can burn out the resistor or change its value.) Create the circuit shown below...
A circuit consists of a 6 ohm resistor, a 0.3 farad capacitor, and an AC voltage...
A circuit consists of a 6 ohm resistor, a 0.3 farad capacitor, and an AC voltage source supplying V(t) = 120 cos(10 t) volts. 1. Write the differential equation for the charge on the capaciton q'+0.55 0.56 q=20 cos(10t) X 2. Write a formula for the solution, assuming q(0) 0 q(f) =
ng off a long time. Find 6) For the following circuit, the voltage source turns on...
ng off a long time. Find 6) For the following circuit, the voltage source turns on a time zero after bei (a) at t 0+ the inductor current i(O+) and its rate of change, (b) at t = 0+ the capacitor voltage vo-) and its rate of change, du (Do not write a differential equation or solve for voltage or current as functions of time.) dt t0+ 4012 10.2 211(1) A 10u() V tz 0 lot) 1O Carm
2. This problem is about an RLC circuit, which involves a resistor (of resistance R ohms),...
2. This problem is about an RLC circuit, which involves a resistor (of resistance R ohms), an inductor (of L henries), and a capacitor (of C farads). There is also a voltage source (such as a battery) providing E(t) volts at time t. 0 Switch When the switch is closed there is a current of I(t) amperes. With the help of Kirchhoff's laws one can derive an ODE for I = I(t): LI" + RI' + + I = E'(t)...
7 A circuit consists of a resistor of resistance R, and a capacitor of capacitance C, connected in series, and is described by the first order differential equation - + y = E where E is the constant e.m.f. and v is the voltage across the capacitor. Given that v(O) = 0, show by using the integrating factor method that v = E(1 - e-t/(RC))
uestion 3: (10 points) n the RC circuit in the figure, Ri = 10 KQ, R2 = 30 KO, and C 6 uF. aswer the following questions, ) What is the equivalent resistor R12 to R and R2? 2) Find the differential equation relating the output voltage Vout to the input voltage 3) What is the order of the system? 4) What is the time constant t? 5) For step input Vin = 10V, find an expression for the output...
04) The RC Circuit shown below includes both a fixed resistor and a potentiometer. By turning the knob on the potentiometer, the resistance between the fixed resistor and the capacitor can be changed within the range of 0 to 20 ko. a. Is this a lowpass or high pass configuration? R = 10 kn Rror = 20 k2 C = 10 uF b. Find an expression for the voltage across the capacitor Vou(t) to a unit voltage step (the voltage...
The circuit below can be used to simulate/measure the equivalent resistance of a circuit. The voltage from V, to ground will be the equivalent resistance because V-IR and in this case the current source ll is equal to 1 Amp. Note that in general Amp.s not used by a resistance meter as it can cause a too much power to be dissipated by the resistor which can burn out the resistor or change its value.) Create the circuit shown below...
A circuit consists of a 6 ohm resistor, a 0.3 farad capacitor, and an AC voltage source supplying V(t) = 120 cos(10 t) volts. 1. Write the differential equation for the charge on the capaciton q'+0.55 0.56 q=20 cos(10t) X 2. Write a formula for the solution, assuming q(0) 0 q(f) =
ng off a long time. Find 6) For the following circuit, the voltage source turns on a time zero after bei (a) at t 0+ the inductor current i(O+) and its rate of change, (b) at t = 0+ the capacitor voltage vo-) and its rate of change, du (Do not write a differential equation or solve for voltage or current as functions of time.) dt t0+ 4012 10.2 211(1) A 10u() V tz 0 lot) 1O Carm
2. This problem is about an RLC circuit, which involves a resistor (of resistance R ohms), an inductor (of L henries), and a capacitor (of C farads). There is also a voltage source (such as a battery) providing E(t) volts at time t. 0 Switch When the switch is closed there is a current of I(t) amperes. With the help of Kirchhoff's laws one can derive an ODE for I = I(t): LI" + RI' + + I = E'(t)...
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