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Lesson 6
Direct Current Circuits
Electro Motive Force
Internal Resistance
Lesson
6 and Parallel
Resistors
in Series
Kirchoffs Rules
Topics
RC Circuits
Charging
Discharging Capacitors
Electrical Instruments
Galvanometer
Ammeter
Voltmeter
Wheatstone Bridge
Potentiometer
Electro Motive Force (emf)
EMF I
Source of emf is any device that increases the
potential energy of charges circulating in a circuit.
Electric Potential increases by the emf E as charge
goes from negative to positive plate of battery.
EMF II
EMF
Work Done per unit charge by
electrical pump
e
dW
=
dQ
Charge Pump
Current flowing internally in battery
feels resistance
Internal resistance, r
Flowing positive charges (current)
experience drop of electric potential
in resistor
V=IR
+
R
-
Charge Pump
Internal Resistance
-
-
+ +
-
+
Terminals
Terminal Potential Difference
V = E - Ir
Picture
e
 Ir
V =
= IR
Power Vand
Internal
= IR  Ir
e
Resistance
e
I=

Rr
Thus power generated by emf
e
I
=
e
2
Rr
Combinations of
Combination
of
Resistors
Resistors
Parallel
same electric potential felt by
each element
Series
electric potential felt by the
combination is the sum of the
potentials across each element
V = V 1  V 2 = IR1  IR2
Series
V = I  R1  R2  = IReq
Req =

i
Ri
V

R1
 1
1 
I = V 

 =
R2 
R1
1
1
1
=

Req
R1
R2
I = I1  I2 =
Parallel
1
=
Req

i
1
Ri
V
R2
V
Req
Kirchoff’s Rules
The sum of the currents
entering a junction must
equal the sum of the
currents leaving
Conservation of Charge
Kirchoffs Rules I
Kirchoffs Rules II
The Sum of the Potential
Differences around a
closed circuit loop must
be zero
Conservation of Energy
Picture
RC Circuits
Non Steady State
Non Equilibrium
Current varies with time
RC circuits
Picture
Charging I
When switch is closed
q
e  IR  = 0
C
Thus at time t = 0, q 0  = 0
I0
e
= I 0  =
R
When capacitor is fully charged the current
in the circuit is zero and the charge on the capacitor is a max
Q = qmax = Ce
e
d
dt

 e

 IR


 IR

q
C
= 0

q
dI

 = 0 = 0  R
C 
dt
dI
I
 R

= 0
dt
C
dI
1

= 
dt
I
RC
Charging II


I
dI
I
I
= 
1
RC
0
 I 
t
 = 
ln 
 I 0 
RC
I t  =
R
e

t
RC
1
C
dq
dt
t
dt
0
I t = I 0e

e


t
RC
I t  =
e
e
R

t
RC
Charging
III
e
dq =
dt
R
e
 dq =

q
dq =
R
 q t  = C e
R
e
e

e
0

1 


e

t
RC

t
RC

t
RC
dt
t
e

t
RC
dt
0


 = Q 1 




e

t
RC




Time
Constant

Time Constant
 = RC
V Q Q
  =  RC =  = Q = s
I V
s
Discharging
Discharging I
+Q
-Q
q
=
IR
from Kirchoff
C
dq
=

I
the rate of decrease of charge
dq
q
R
=
dt
C
dq
1
=
dt
q
RC
Discharging II

q
Q
dq
1
= 
q
RC

t
dt
0
q 
t
ln   = 
Q 
RC
qt  = Qe

dq
Q
I t  = 
=
e
dt
RC

t
RC
t
RC
= I0 e

t
RC