# Charging C

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Education

Published on March 24, 2009

Author: christaines

Source: slideshare.net

Lecture 21 - Capacitors in circuits Charging a capacitor (semi-qualitative). Charging a capacitor (quantitative). The time constant. Discharging a capacitor. Energy Considerations. The End

Charging a capacitor (semi-qualitative).

Charging a capacitor (quantitative).

The time constant.

Discharging a capacitor.

Energy Considerations.

The End

Charging a capacitor - diagram.

Charging a capacitor (semi-qualitative). At time t=0 the switch is closed, with the capacitor initially uncharged. A current will flow  =V c +V R =I 0 R , as initially V c =0. Thus the initial current is I 0 =  /R . Now a charge begins to build on the capacitor, introducing a reverse voltage. The current falls, and stops when the P.D. across C is  . Final charge is given by &quot; Q=CV &quot; => Q 0 =C  .

At time t=0 the switch is closed, with the capacitor initially uncharged.

A current will flow  =V c +V R =I 0 R , as initially V c =0. Thus the initial current is I 0 =  /R .

Now a charge begins to build on the capacitor, introducing a reverse voltage. The current falls, and stops when the P.D. across C is  .

Final charge is given by &quot; Q=CV &quot; => Q 0 =C  .

Charging a capacitor (quantitative). Apply Kirchoff's loop rule.

Apply Kirchoff's loop rule.

Charging a capacitor (cont) Where Q 0 = C  = the final charge on the capacitor.

Where Q 0 = C  = the final charge on the capacitor.

Charging a capacitor (cont). To find the current, differentiate since I=dQ/dt . By considering time zero, when the current is I 0 ,

To find the current, differentiate since I=dQ/dt .

By considering time zero, when the current is I 0 ,

The time constant. The time constant  =RC . The units are seconds ( t/RC is dimensionless). The time taken for the charge to rise to 1-(1/e) of the final value in the circuit. The current to fall by 1/e of its initial value.

The time constant  =RC .

The units are seconds ( t/RC is dimensionless).

The time taken for the charge to rise to 1-(1/e) of the final value in the circuit.

The current to fall by 1/e of its initial value.

Discharging capacitor - diagram.

Discharging a capacitor. Apply Kirchoff's loop rule.

Apply Kirchoff's loop rule.

Discharging a capacitor (cont) To find the current...

To find the current...

Discharging a capacitor (cont) To find the current... Note the sign, the current flow has reversed! But, when t=0, I=I 0 , so

To find the current...

Note the sign, the current flow has reversed!

But, when t=0, I=I 0 , so

Energy Considerations. During charging, a total charge Q=C  flows through the battery. The battery does work W=Q 0  =C  2 . The energy stored in the capacitor is ½ QV= ½ Q 0  = ½ C  2 . Where's the other half?

During charging, a total charge Q=C  flows through the battery.

The battery does work W=Q 0  =C  2 .

The energy stored in the capacitor is ½ QV= ½ Q 0  = ½ C  2 .

Where's the other half?

Energy considerations (cont). Solve by setting x=2t/RC . Which, when added to the energy stored on the capacitor, equals the work done by the battery.

Solve by setting x=2t/RC .

Which, when added to the energy stored on the capacitor, equals the work done by the battery.

Finally… E-M depends a lot on integrals, vectors etc. shows how useful they are. It is one of the foundations of physics but: it can be rather formal, encouraging the precise thinking that we expect of any academic training; it is rather far removed from the everyday, but that develops the imagination we expect from a physicist.

E-M depends a lot on integrals, vectors etc. shows how useful they are.

It is one of the foundations of physics but:

it can be rather formal, encouraging the precise thinking that we expect of any academic training;

it is rather far removed from the everyday, but that develops the imagination we expect from a physicist.

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