2.5 - Capacitance
● Capacitors store (electrical) energy BUT NOT charge
Q
● C=
V
Energy storage by capacitors
1 1 1 Q2
● E= QV (¿ C V 2= )
2 2 2 C
○ Essentially area under voltage (y)-charge (x) graph
Exponential function
● discharge
t
V RC
○ Making V0 the subject: V 0= −t
=V e /¿
RC
e
−t
V V −t
○ Making R the subject: =e RC , ln ( )=
V0 V 0 RC
−t t
R= = /¿
V V
C ln( ) C ln( 0 )
V0 V
−t t
V −t C= = /¿
○ Making C the subject: ln ( )= , V V0
V 0 RC R ln( ) R ln ( )
V0 V
●
● Time constant: τ = RC
1
● Capacitors store (electrical) energy BUT NOT charge
Q
● C=
V
Energy storage by capacitors
1 1 1 Q2
● E= QV (¿ C V 2= )
2 2 2 C
○ Essentially area under voltage (y)-charge (x) graph
Exponential function
● discharge
t
V RC
○ Making V0 the subject: V 0= −t
=V e /¿
RC
e
−t
V V −t
○ Making R the subject: =e RC , ln ( )=
V0 V 0 RC
−t t
R= = /¿
V V
C ln( ) C ln( 0 )
V0 V
−t t
V −t C= = /¿
○ Making C the subject: ln ( )= , V V0
V 0 RC R ln( ) R ln ( )
V0 V
●
● Time constant: τ = RC
1
