RC Circuits RC Circuits Charging At t=0, capacitance is uncharged - - PDF document

RC Circuits

RC Circuits – Charging

 C R

At t=0, capacitance is uncharged and Q=0 (initial condition). At t=0, switched is closed, it the capacitor has no charge, it behaves like a conductor and I=/R. After the capacitor is completely charged, Q=C , VC=  and VR=0. I=0 and the capacitors behave like an insulator.

RC Circuits – Charging

 C R

) e 1 ( C q C

• K

K C q 0, At t e K C q ) e (K Ke C

• q

K' CR t

• )

C

• q

n( dt CR 1

• C
• q

dq dt q)

• (C

dq CR t d q d R C q IR C q

CR t

• CR

t

• K'

CR t

• 

                                      ) e

• (1

C q V e IR V e R e CR C t d dq I

CR t

• C

CR t

• R

CR t

• CR

t

• 

           

Integration constant VR + VC = 

RC time constant

=RC is known as the RC time constant. It indicates the response time (how fast you can charge up the capacitor) of the RC circuit.

e R I

CR t

• 

 R I  

t

R 37 . ~ R e I

1

• 

 

t=RC

) e 1 ( C q

CR t

• 

   C q 

t

  C 63 . ~ C ) e 1 ( q

• 1

 

t=RC

37 . e 2.72 e

1

• 

 707 . 2 1 1.414 2  

Nothing to do with RC circuits

RC Circuits – Discharging

C R

At t=0, capacitance is charged with a charge Q (initial condition). At t=0, switched is closed, the capacitor starts to discharge. After the capacitor is completely discharged, Q=0, VC= 0, VR=0 and I=0.

RC Circuits – Discharging

CR t

• CR

t

• K'

CR t

• Qe

q K Q Q q 0, At t e K q ) e (K Ke q K' CR t

• q

n dt CR 1

• q

dq dt q

• dq

CR ) t d q d

• (I

t d q d R C q IR C q                         

CR t

• C

CR t

• R

CR t

• e

C Q C q V e C Q IR V e RC Q t d dq I          

Integration constant VR + VC = 0

C R

In Summary

For both charge and discharge, Q, I, VC, and VR must be one of the following two cases:

t t

RC t

• 0e

y y 

y can be Q, I, VC, or VR y y0 y y

) e

• (1

y y

RC t

• 



Class 26: Magnetic force acting on a moving point charge

Magnetic Field

• 1. All single magnets have two poles, N and S.
• 2. Externally, magnetic field lines come out from the N pole and getting into the S pole.
• 3. Between two magnets, like poles repel and unlike poles attract.
• 4. The geographical north pole of earth is actually the S pole of a bar magnet.
• 5. We will explain why there is magnetic field later.

cross product between two vectors



bc

• ad

d c b a B B A A k ˆ B B A A j ˆ B B A A i ˆ B B B A A A k ˆ j ˆ i ˆ B A

y x y x z x z x z y z y z y x z y x

        B A    A  B 

Direction: Magnitude:

 sin | B || A | B A      

From class 3

A common symbol

• r
• r

A vector perpendicular and pointing into the screen /paper. A vector perpendicular and pointing out of the screen /paper.

From class 3

Magnetic Force Acting on a Moving Charge

• 1. Unit of magnetic field is Tesla (T).
• 2. If there is magnetic field, only under two conditions the magnetic force
• n the charge particle will be zero: (i) the particle is not moving (v=0), or

(ii) it is moving in parallel or antiparallel to the magnetic field (sin=0).

• 3. The magnetic force is always perpendicular to the magnetic field and the

velocity.

• 4. The magnetic force does no work because .
• 5. If you want to determine the direction acting on a negative charge

particle, treat it like a positive charge first, then reverse the force direction at the end.

When a charge particle moves in a magnetic field B, there will be magnetic force acting on the particle: B v F `

B v q FB     

v FB    