Question

In: Physics

Consider a RC circuit. At time t=0, the circuit is closed. ( a) Draw how the...

Consider a RC circuit. At time t=0, the circuit is closed. ( a) Draw how the current behaves with time. (b) What about the power dissipated by the resistor ? (also draw it as a function of t)

Solutions

Expert Solution

Kirchhoff’s Loop Rule

At t=0, there is no charge on (hence no potential across) the capacitor so at the “instant” the switch is closed, we expect a current of I0=ε/R (voltage drop is only across the resistor). As the capacitor charges, we expect the current to fall.

   

                     

Close Switch at t=0

Charge will flow on the capacitor and the current will decrease until we reach i = 0, then:

                 

the final value charge, Qf does not depend on R

     

                                     

                                 

     

This is a differential equation. We can rearrange and integrate to find what we need.

                                     

                                   

       

                                

      Taking the exponents (inverse log) both sides

                              

                         

                          

Taking the time derivative, to get the instantaneous , current, i  

                           

                            

                      

Solution(B)

            

              

                        

   

  

Kirchhoff’s Loop Rule

At t=0, there is no charge on (hence no potential across) the capacitor so at the “instant” the switch is closed, we expect a current of I0=ε/R (voltage drop is only across the resistor). As the capacitor charges, we expect the current to fall.

   

                     

Close Switch at t=0

Charge will flow on the capacitor and the current will decrease until we reach i = 0, then:

                 

the final value charge, Qf does not depend on R

     

                                     

                                 

     

This is a differential equation. We can rearrange and integrate to find what we need.

                                     

                                   

       

                                

      Taking the exponents (inverse log) both sides

                              

                         

                          

Taking the time derivative, to get the instantaneous , current, i  

                           

                            

                      

Solution(B)

            

              

                        

   

                                  

                                    

  

                                    


Related Solutions

Consider a RC circuit. At time t = 0, the circuit is closed. (a) Draw how...
Consider a RC circuit. At time t = 0, the circuit is closed. (a) Draw how the current behaves with time (b) What about the power dissipated by the resistor? (also draw it as a function of t)
Given a RC circuit in series , at time t=0, power supply 4v is connected to...
Given a RC circuit in series , at time t=0, power supply 4v is connected to the circuit causing charging of capacitor, determine at instant 8 seconds : Where C = 10 mF, R = 4 kOhms, and consider all initial values equal to ZERO. a) Tension on capacitor; b) Tension on resistor; c) total current.
Solve the equation for a charging capacitor (Vc = Vs(1-e^(t/t))) for an RC Circuit for the ratio of the time (t) to the RC time constant (t):
it is rc time constant problem. 1. Solve the equation for a charging capacitor (Vc = Vs(1-e^(t/t))) for an RC Circuit for the ratio of the time (t) to the RC time constant (t): Show all steps. 2. Using the answer to Part 1, calculate the fraction of a time constant (t) to charge an initially uncharged capacitor to 10% of the source voltage (Vs). Show all steps. 3. Using the appropriate answers from Part 1, calculate the fraction of...
The figure below shows an RC circuit. The capacitor is initially uncharged. At t = 0,...
The figure below shows an RC circuit. The capacitor is initially uncharged. At t = 0, the switch is closed to point a. Find the time it takes for the capacitor voltage to reach one third the battery voltage. Use the figure above. In the figure, the switch has been at point a for a long time and the capacitor voltage is equal to the battery voltage. At t = 0, the switch is moved to point b. Find the...
Consider an RC circuit with resistance R and capacitance C. The circuit is stimulated with a...
Consider an RC circuit with resistance R and capacitance C. The circuit is stimulated with a pulse of amplitude A and width T. The purpose of this study is to understand what happens to the impulse response, capacitor voltage, and resistor voltage for various resistor values: 600 ?, 1000 ?, and 1200 ?. The name of the MATLAB script will be called project2a. Excite the circuit with a rectangular pulse voltage of amplitude=5 V and pulse width of 10 ms....
show that the relaxation time for a heavily damped rlc circuit is RC
show that the relaxation time for a heavily damped rlc circuit is RC
Draw phasor diagrams for the following circuits. A) For the first circuit: Analyze a series RC...
Draw phasor diagrams for the following circuits. A) For the first circuit: Analyze a series RC circuit. So an emf with frequency w and peak voltage V connected in series to a resistance with peak voltage V_R and a capacitor with a peak votage V_C. B) For the second one, do a parallel RL circuit. Same emf as above, but resistance R in parallel to inductor with inductance L. Step by step Thank you
In an RC circuit the time constant is defined as Select one: True False
In an RC circuit the time constant is defined as Select one: True False
In an RC circuit as depicted in the figure above, what happens to the time required...
In an RC circuit as depicted in the figure above, what happens to the time required for the capacitor to be charged to half its maximum value if either the resistance or capacitance is increased with the same applied voltage? (Select all that apply.) A.Increasing the resistance increases the time. B.Increasing the resistance decreases the time. C.Increasing the capacitance increases the time D.Increasing the capacitance decreases the time.
What is a time constant and what does it mean for a decaying RC circuit?
What is a time constant and what does it mean for a decaying RC circuit?
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT