Book Reference : Pages 100-101Book Reference : Pages 100-101

1.1. To look at how capacitor discharge may be To look at how capacitor discharge may be examined in the labexamined in the lab

2.2. To revisit capacitor applications (particularly To revisit capacitor applications (particularly timing circuits)timing circuits)

3.3. To understand charging a capacitor through To understand charging a capacitor through a fixed resistora fixed resistor

When measuring the voltage across the resistor during discharge When measuring the voltage across the resistor during discharge one can use a oscilloscope, multimeter, or one can use a oscilloscope, multimeter, or data logger data logger as long as as long as it has a very high resistance to reduce the current flow through itit has a very high resistance to reduce the current flow through it

V0

Switch

Charge Discharge

Either way we plot a graph of the results to establish Either way we plot a graph of the results to establish the time constant “RC”. Data loggers are ideal for this the time constant “RC”. Data loggers are ideal for this application and simplify the process application and simplify the process

C Fixed resistor R

OR OR

As an example of using capacitor discharge as a timing As an example of using capacitor discharge as a timing mechanism consider a burglar alarm which has a delay mechanism consider a burglar alarm which has a delay between being trigged and sounding the sirenbetween being trigged and sounding the siren

V

Switch

Charge

Discharge

The bell electronics will ring the bell if the voltage across The bell electronics will ring the bell if the voltage across the capacitor drops below a predetermined level once it the capacitor drops below a predetermined level once it has been trigged by changing the switch location. The has been trigged by changing the switch location. The delay can be selected by choosing the size of R and C (as delay can be selected by choosing the size of R and C (as in the time constant RC) in the time constant RC)

CR

Charging a capacitor through a fixed resistor is Charging a capacitor through a fixed resistor is similar to discharging (in the opposite sense)similar to discharging (in the opposite sense)

V0

Switch

C

Fixed resistor R

1.1. When the switch is closed, initially When the switch is closed, initially a significant current flowsa significant current flows

2.2. As the capacitor charges, the pd As the capacitor charges, the pd across it increases and the current across it increases and the current flow reducesflow reduces

3.3. Once fully charged the pd across Once fully charged the pd across the capacitor is equal to Vthe capacitor is equal to V00 and and current no longer flowscurrent no longer flows

As the voltage increases the charge increases in the As the voltage increases the charge increases in the same manner (since Q same manner (since Q V from Q = CV)V from Q = CV)

In this case the time constant RC In this case the time constant RC is at 0.63 Qis at 0.63 Q00 (or V (or V00) i.e. (0.37 ) i.e. (0.37 more to reach Qmore to reach Q00 ( or V ( or V00))))

Charge (Q) and pd (V) graphs Charge (Q) and pd (V) graphs have exactly the same shapehave exactly the same shape

The current graph is gradient of The current graph is gradient of the charge graph (since I=Q/t or I the charge graph (since I=Q/t or I =V/R) & hence decreases =V/R) & hence decreases exponentiallyexponentially

Since it is a series circuit, at any given Since it is a series circuit, at any given time during charging....time during charging....

VV00 = resistor pd + capacitor pd = resistor pd + capacitor pd

This can be expanded asThis can be expanded as

VV00 = IR + Q/C = IR + Q/C

Assuming initially the capacitor has no Assuming initially the capacitor has no charge then the initial current Icharge then the initial current I00 is is

II00 = V = V00 / R / R

and at any given time :and at any given time :

I = II = I00 e e–t/RC–t/RC

An uncharged 4.7An uncharged 4.7F capacitor is charged to a pd of 12V F capacitor is charged to a pd of 12V through a 200through a 200 resistor and then discharged through a resistor and then discharged through a 200k200k. Calculate :. Calculate :

The initial charging current The initial charging current [60mA][60mA]

The energy stored in the capacitor at 12V The energy stored in the capacitor at 12V [0.34mJ][0.34mJ]

The time taken for the pd across the capacitor to fall The time taken for the pd across the capacitor to fall from 12v to 3v from 12v to 3v [1.4s][1.4s]

The energy lost by the capacitor in this time The energy lost by the capacitor in this time [0.32mJ][0.32mJ]

A 68A 68F capacitor is charged by connecting it to a 9V F capacitor is charged by connecting it to a 9V battery & then discharging it through a 20kbattery & then discharging it through a 20k resistor. resistor. Calculate :Calculate :

The initial charge stored The initial charge stored [0.61[0.61C]C]

The initial discharge current The initial discharge current [0.45mA][0.45mA]

The pd and the discharge current 5s after the start The pd and the discharge current 5s after the start of the discharge of the discharge [0.23V, 11[0.23V, 11A]A]

A 2.2A 2.2F capacitor is charged to a pd of 6V & then F capacitor is charged to a pd of 6V & then discharging it through a 100kdischarging it through a 100k resistor. Calculate : resistor. Calculate :

The charge & energy stored at a pd of 6V The charge & energy stored at a pd of 6V [13[13C, 40C, 40J]J]

The pd across the capacitor 0.5s after discharge The pd across the capacitor 0.5s after discharge started started [0.62V][0.62V]

The energy stored at this time The energy stored at this time [0.42[0.42J]J]