Unit-5
Steady electric current and circuit properties
5.1 Basic principles
1. Electric current
 w/n a conductor is connected to a source of voltage or battery the free electrons in it will
undergo an ordered or directional motion forming electric current
 it is given as , I = Q /t
 its si-unit is ampere A
 1A = 6.25ₓ1018 electrons / second =1C / s
 1e = 1.6ₓ10-19C
2. Resistance, resistivity, and conductivity
2.1. Conductivity
(6)
 It measures material ability to allow electric current through it
2.2. Resistivity (ᵨ)
 It measures material ability to resist the flow of electron in it
 Conductivity and resistivity are inverse proportional
ᵟ=1/ᵨ
 Its si unit is Siemens per meter
2.3. Resistance ( R )
 It is a property of a material to control amount of current
 It is electrical device to control amount of current
 It is given , R = ᵨ L /A, R = V / I
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Drift velocity and current density
Drift velocity ( Vd )
It is average velocity of an electron in moving through a conductor
Due to collision they do not move straight lines along the conductor instead they move or
undergo a zigzag motion
Electric field in a wire gives electrons a drift velocity
2. Current density ( J)
 It described as J= I/ A and J=ᵟ E
I=∆Q/∆t
∆Q = n q A ∆X = n q A Vd ∆t
Therefore. Vd = J /n q , where ,n-is number of charge
Electromotive force and internal resistance
Sources of electromotive force
 Cell, or battery transforms non electrical energy ( chemical in cell or battery to electrical)and
generator transforms mechanical in to electrical energy
 Sources of emf are energy converters
 r is internal resistance in the cell
Vd = I r
 terminal voltage is voltage out of the cell
Vt =I R
 therefore , some energy is lost in the cell due to heat
Ԑ= Vt +Vd
I = Ԑ /R+r
 remaining potential is , Vt = Ԑ - Vd
Power in an electrical circuit
 it is a rate at w/c electrical energy is converted in to heat
 it is given as
P= W/t =V I , V=I R , I=V/R , W = Q V
P= R I2= V2/R
Combining resistors
1. In series
 It given as
1. IT =I1=I2=I3=In
2. VT= V1+V2+V3+ +Vn
3. V=I R
4. RT=R1+R2+R3+ +Rn
2. In parallel
 It is given as
1. VT =V1=V2=V3=Vn
2. IT=I1+I2+I3+ +In
3. I=V/R
4.1/RT =1/R1+1/R2+1 / R3 + +1/ Rn
5.2 Kirchhoff’s rules
 It used to solve complicated circuits
 It is valid in any junction and loop
1.1st rule (junction)
 States that the algebraic sum of the currents entering any junction point in a circuit is zero
 This means that the sum of currents entering any junction point is equal to the sum of the
currents leaving the same junction point
 It is based on the law of conservation of charge
I in = I out
 About direction, first take assumption. Second if your answer is opposite to the actual current
direction , a negative current will be result
2.2nd rule (loop)
 States that the algebraic sum of the potential difference ( voltage) around any closed loop is
equal to zero
 This means that the algebraic sum of the emf s in any loop equals the algebraic sum of the
voltage in the same loop
 Given as
Sum of emf = sum of IR
 It is based on principle of conservation of energy applied for electric circuit
Sign convention for voltage
 If you move as follows ,
1. For voltage drop
a. In the direction of current , V = -I R
b. Opposite to direction of current , V= I R
2. For emf
a. In the direction of current , V = emf
b. Opposite to direction of current, V= -emf
5.3 Measuring instruments
1. Ammeter
 It used to measure current at any branch
 It Connected in series with resistor
 Resistance of ammeter should be low as possible
2. Voltmeter
 It used to measure the voltage drop across some part of a circuit
 It connected parallel to with resister
 Resistance of voltmeter should be high as possible
3. Galvanometer
 It is a moving coil meter
 It used to sensitive measurement of electric current ( very small )
3.1 Galvanometer to measure large currents
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It is converted in to ammeter by placing a resistor in a parallel with the Galvanometer
Such resistor is called a Shunt ( small resistor)
It should be small resistance
It acts as ammeter
Given as
Vg = Ig . Rg
Vs = Is .Rs
I = Is + Ig , Is = I-Ig
Rs = Ig . Rg / I-Ig
3.2 Galvanometer to measure large voltmeters
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It connected to large resister with galvanometer in series
It is called multiplier resister
It acts as voltmeter
It given as
V = VR +Vg
R = v-I Rg /I
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5.4 The Wheatstone bridge
It is a type of bridge circuit
It has four resistors R1, R2, R3,& Rx connected end to end
Values of R1 &R2 are precisely known
Value of Rx is unknown resistor w/ c is measured
Value of R3 is variable
w/n R3 is adjusted so that there is no current through the galvanometer
the bridge said to be balanced
 w/n Ig=0 , I1 and I2 are in series , I1=I2 and similarly I3=Ix
 potential difference b/n A and B , VAB= 0, VA=VB ,therefore
VAC = VBD
I1 R1=I3 R3, are parallel
equ.1
 Similarly , VAD = VCB
I2 R2 = IX RX , are in parallel equ. 2
 Divide equ. ½ , you get
R1/R2 =R3/RX
RX = R2 R3 /R1
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The potentiometer
It is potential divider circuit
It is used to measure emfs and potential differences
Known resistances are R1 and R2
Test cell is emf is determined
b/c it is parallel to R1
given as , emf = V1 = V ( R1 / R1+R2 )
I1 = V1/R2
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Comparing the emf of two cells using a potentiometer
Instead of the two resisters R1 & R2 as above fig , a wire of uniform cross section can be used
as in fig below
Emf 1 is one of the two cells for comparison
w/n the galvanometer read zero : emf 1˷l1
Then disconnect the cell emf1 from the circuit and replace it by emf 2 , the other cell for
coparison
Again move the pointer p until the galvanometer reads zero
Then measure the length of the wire from A to p ( l2 ) , where emf 2˷l2
Then , emf1/emf2 =l1/l2.