Homework Answers
By KVL across second loop,
q/C - iR - Vb = 0
q/C - R*dq/dt - Vb = 0
dq/dt = q/RC - Vb/R
dq/[q/RC - Vb/R] = dt
after integrating
RC* ln(q/RC - Vb/R) = t
After applying the limit that q at t=0 will be CVa and at some time t it will be CV,
CV/RC - Vb/R)/(CVa/RC - Vb/R) = e^(-t/RC)
(V - Vb)/(Va - Vb) = e^(-t/RC)
V = Vb + (Va - Vb)e^(-t/RC)
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Question 3 0/1 pts Consider the circuit shown. The switch is initially open and the capacitor...
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In the circuit of the figure below, the battery emf e m f is 60 V,...
In the circuit of the figure
below, the battery emf e m f is 60 V, the resistance R is 150 Ω,
and the capacitance C is 0.500 µF. The switch S is closed for a
long time interval, and zero potential difference is measured
across the capacitor. After the switch is opened, the potential
difference across the capacitor reaches a maximum value of 150 V.
What is the value of the inductance?
In the circuit of the figure below,...
ln the figure below you see a circuit with a battery (V), a capacitor (C), and...
ln the figure below you see a circuit with a battery (V), a
capacitor (C), and two resistors (R1 and R2). The circuit has a
switch that can be in two positions: switched to touch point A or
switched to touch point B. By setting first the switch to A you can
charge the capacitor, and then switching it to B you discharge the
capacitor through the resistor. (This is the simple mechanism
behind a camera flash, you can imagine...
r R ε с [7 points] 14. In the circuit shown above a battery with emf...
r R ε с [7 points] 14. In the circuit shown above a battery with emf & and internal resistance r may be connected to a capacitor C through switch S. The switch may also connect the capacitor to resistor R. The capacitor is initially uncharged. Express your final answers only in terms of the variables €.r.C, R, and any necessary constants, as appropriate. a) At time t = 0, the switch is moved from the right to the left....
In the circuit of the figure below, the battery emf E is 50 V, the resistance...
In the circuit of the figure below, the battery emf E is 50 V, the resistance R is 210 Q, and the capacitance C is 0.500 pF. The switch S is closed for a long time interval, and zero potential difference is measured across the capacitor. After the switch is opened, the potential difference across the capacitor reaches a maximum value of 150 V. What is the value of the inductance? Н С
Question 4a Consider the LRC circuit shown below. At 0, the switch S is closed and a voltage Va-V...
Question 4a Consider the LRC circuit shown below. At 0, the switch S is closed and a voltage Va-Vr = Vo cos wt is applied between A and F A -000i R. The equation describing the evolution of Q(t), the charge on the capacitor is CGiven Q0) amd #(o) - 0), the geteral solution of 1) may be written as (0), the general solution of (1) may be written as where Qc(t) as t0o, so after a long time, 2L...
Problem Consider the circuit shown below, in which the switch instantaneously moves back and forth between...
Problem Consider the circuit shown below, in which the switch instantaneously moves back and forth between contacts A and B, spending 2 seconds in each position. Thus, the capacitor repeatedly charges for 2 seconds and then discharges for 2 seconds. Assume that uc (0)-0 V and the switch moves to position A at -0s. a) Find the voltage across the capacitor vc for t = 2 s, t = 4 s, t = 6 s, and t b) Sketch vc...
This lab involves an animation of an RC circuit. By clicking on the connect battery link...
This lab involves an animation of an RC circuit. By clicking on
the connect battery link below the animation, you close switch 1
and open switch 2 connecting a 40V battery to the resistor and
capacitor in series. By clicking on the disconnect battery link,
you close switch 2 and open switch 1 eliminating the battery from
the circuit and connecting the resistor and capacitor in series. On
the right hand side a graph of the current vs. time through...
(12 pts) In the circuit below the capacitor is fully charged to 12.0 V. Switch S is next flipped down for discharge of the capacitor. (a) Show the new switch position on the diagram and the current flow direction during discharge. (b) Sketch the voltage Vc across the capacitor C (during discharge) as a function of time t on the graph below. (c) Calculate the time constant for the discharge from the given R and C values. 8. Graph of...
Problem 7 A resistor with resistance R, battery with voltage AV, capacitor with capacitance C, and switch are connected in series. The switch is closed at t = 0. The time constant of the circuit is T. What is the initial voltage across the resistor immediately after the student is closed? Select One of the Following: (a) o (b) AV (c) TAV (d) AV/T (e) AV/(R+C) Problem 8 A capacitor is charged to potential difference V and then allowed to...
Question 3 0/1 pts Consider the circuit shown. The switch is initially open and the capacitor completely discharged. All resistors have a resistance R and the capacitor has a capacitance C. The battery is ideal and provides a potential V The switch is closed at time 0, allowing current to flow. Which graph most appropriately represents the current through the battery (indicated by an arrow) as a function of time? Time VIR VIR Time
In the circuit of the figure
below, the battery emf e m f is 60 V, the resistance R is 150 Ω,
and the capacitance C is 0.500 µF. The switch S is closed for a
long time interval, and zero potential difference is measured
across the capacitor. After the switch is opened, the potential
difference across the capacitor reaches a maximum value of 150 V.
What is the value of the inductance?
In the circuit of the figure below,...
ln the figure below you see a circuit with a battery (V), a
capacitor (C), and two resistors (R1 and R2). The circuit has a
switch that can be in two positions: switched to touch point A or
switched to touch point B. By setting first the switch to A you can
charge the capacitor, and then switching it to B you discharge the
capacitor through the resistor. (This is the simple mechanism
behind a camera flash, you can imagine...
r R ε с [7 points] 14. In the circuit shown above a battery with emf & and internal resistance r may be connected to a capacitor C through switch S. The switch may also connect the capacitor to resistor R. The capacitor is initially uncharged. Express your final answers only in terms of the variables €.r.C, R, and any necessary constants, as appropriate. a) At time t = 0, the switch is moved from the right to the left....
In the circuit of the figure below, the battery emf E is 50 V, the resistance R is 210 Q, and the capacitance C is 0.500 pF. The switch S is closed for a long time interval, and zero potential difference is measured across the capacitor. After the switch is opened, the potential difference across the capacitor reaches a maximum value of 150 V. What is the value of the inductance? Н С
Question 4a Consider the LRC circuit shown below. At 0, the switch S is closed and a voltage Va-Vr = Vo cos wt is applied between A and F A -000i R. The equation describing the evolution of Q(t), the charge on the capacitor is CGiven Q0) amd #(o) - 0), the geteral solution of 1) may be written as (0), the general solution of (1) may be written as where Qc(t) as t0o, so after a long time, 2L...
Problem Consider the circuit shown below, in which the switch instantaneously moves back and forth between contacts A and B, spending 2 seconds in each position. Thus, the capacitor repeatedly charges for 2 seconds and then discharges for 2 seconds. Assume that uc (0)-0 V and the switch moves to position A at -0s. a) Find the voltage across the capacitor vc for t = 2 s, t = 4 s, t = 6 s, and t b) Sketch vc...
This lab involves an animation of an RC circuit. By clicking on
the connect battery link below the animation, you close switch 1
and open switch 2 connecting a 40V battery to the resistor and
capacitor in series. By clicking on the disconnect battery link,
you close switch 2 and open switch 1 eliminating the battery from
the circuit and connecting the resistor and capacitor in series. On
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