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CHAPTER-27
Circuits
1
Ch 27-2 Pumping Charges
 Charge Pump:
 A emf device that maintains
steady flow of charges through
the resistor.
 Emf device does work on charge
carrier by doing work
 Within the emf device , positive
charge carrier moves from
negative terminal (a region of low
electric potential energy) to
positive terminal (a region of high
electric potential energy) against
E field inside the device.
 This energy , which is chemical
energy , is supplied by emf device

=amount of work dW/charge dq
2
Ch 27-3 Work, Energy, and Emf
 Circuit containing two batteries
 For a circuit with two emf with
similar terminal connected net emf
in the circuit is difference of the
two emf and net current direction in
the direction of the stronger emf.
 For a circuit with two emf with
opposite terminal connected net emf
in the circuit is sum of the two emf
and net current direction in the
direction of the any of the emf.
3
Ch 27-4 Calculating the Current in a
Single-Loop Circuit
 Energy Method
 A current i passes through the resistor
R for a time dt sec. Charge dq=idt
passes through the resistor.
 Work done by battery to move this
charge through the resistor dW=dq=
idt
 His work must be equal to thermal
energy dissipated in the resistor
idt=i2Rdt
 =iR and i= /R
 Potential Method
 Potential method involve calculating the
potential difference between two points
V=Vf-Vi when you move in a circuit
 If you move in a circuit clockwise or
anticlockwise in a loop the Vi=Vf

V=0
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Ch 27-4 Calculating the Current in a
Single-Loop Circuit
 Kirchoff’s Loop Rule
 Algebric sum of potential drop V
encountered in a complete traversal of
any loop is zero i.e
For a loop  Vi=0
 Resistance Rule
 For a move through the resistance R
along direction of current i potential
drop V= -iR
 For a move through resistance R in
direction opposite to current i potential
drop V= +iR
 EMF Rule:
 For a move through emf device along
direction of emf arrow potential drop
V= +
 For a move through emf device opposite
to direction of emf arrow potential
drop V= -
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Ch 27-4 Calculating the Current in a
Single-Loop Circuit
 Potential Method
 Moving in the circuit
clock wise from point a
 V= -iR=0
  = iR and i= /R
6
Ch 27-5 Other Single-Loop Circuit
 Battery Internal Resistance:
 Electrical resistance of the
battery conducting material ,
shown with resistance r in series
with emf 
 Resistance in Series: Resistance in
series can be represented by an
equivalent resistance Req given by :
Req = Ri
7
Ch 27-6 Potential Difference
between two points
 To find potential difference between
any two points in a circuit, start at one
point and traverse the circuit to the
other point , following any path and add
algebraically the changes in potential
you encounter
 To calculate potential difference Vb-Va
start at a then
 Va+ -ir =Vb then
 Vb-Va= V= -ir
A current I through a circuit containing a
battery with internal resistance r and
an external resistor R is i=/(r+R)
 Vb-Va= V= -ir = -r/(r+R)= R/(R+r)
8
Ch 27-6 Potential Difference
between two points
 Grounding a Circuit:
• Connecting the circuit to a conducting path to Earth. The
potential at the grounding point is defined to be Zero.
 Power, potential and Emf
 When a emf device does work to establish a current i in the
circuit, the device transfers its chemical energy to the
charge carrier. It loses power in its internal resistance r.
 Energy transfer rate P from emf to charge carrier
 P= iV=i(-ir)=i-i2r
 Pr=i2r (internal dissipation rate)
 Pemf= i
9
Ch 27-7 Multiloop Circuits
Junction rule:
The sum of currents entering
the junction must be equal
to the currents leaving the
junction
Resistance in Parallel:
 The resistance
connected in parallel
have common voltage
 Resistance in parallel can
be represented by an
equivalent resistance Req
given by :

1/Req =1/ Ri
10
Ch 27-8 Ammeter and Voltmeter
 Ameter A connected in
series while voltmeter
V is used in Paralell.
 If RA is internal
resistance of an
ammeter and RV is
internal resistance of a
voltmeter then :
 RA should be very small
 RV should be very large
11
Ch 27-9 RC Circuits
 Charging the capacitor-time varying
current
 In switch position a current flows
through the resistor R and charge q
start building up on the capacitor
plate. The capacitor voltage V= q/C.
 For fully charged capacitor no
current flows through the resistor
and voltage V across the capacitor
is  then q=C.
 During charging process the loop
rule to the circuit gives:
  - iR-q/C=0 ;  = Rdq/dt+q/C
 q=C(1-e-t/RC)
 Current i=dq/dt= (/R) e-t/RC
 Voltage V=q/c=(1-e-t/RC)
 Time constant =RC
 q=C(1-e-t/RC)=C(1-e-1)=0.63 C
12
Ch 27-9 RC Circuits
 Discharging a capacitor
 In switch position b the
charging equation
  = Rdq/dt+q/C reduces to
 0 = Rdq/dt+q/C ( = 0)
 Then q=q0e-t/RC and q0=CV0
 i=dq/dt=-(q0/RC)e-t/RC=-i0e-t/RC
13
Suggested problems Chapter 27
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