UNIT 5. CURRENT AND RESISTANCE
5.1 Electric current: Electric current at a point in a circuit is the rate at
Formulae
which net charge moves past that
point.
𝒅𝑸
𝒏𝒆
𝑰 = 𝒅𝒕 = 𝒕
Direct current is current
flowing in a direction that does not
Unit is Ampere or C/s.
change with time. The direction of
1 A = 1C/1s
current is defined as the direction in
which positive charge would be
moving.
 Direction of current (+ve to –
ve) is always opposite to that of electrons (- ve to +ve side).
 A current that flows in one direction is called Direct Current (DC) and
the current that changes the direction is called alternating current or AC.
From the experiments,the light bulb shines, even if the battery’s orientation
is reversed. Adding more
bulbs in series, decreases
the brightness of the bulb.
Adding
more
batteries,
increases the brightness of
the bulb. The bulbs will
have the same brightness if
they are connected in parallel.
2. A 100.0 W light bulb draws 0.83 A of current.
1 The current in a light bulb is 0.835 A. How long does
it take for a total charge of 1.67 C to pass through the
How long does it take for 1.9 × 1022 electrons to
pass a given cross-sectional area of the filament?
filament of the bulb?
4. If a metal wire carries a current of 80.0 mA, how
3. In a particular television tube, the beam current is
60.0 µA. How long does it take for 3.75 × 10 electrons
14
to strike the screen?
long does it take for 3.00 × 1020 electrons to pass a
given cross-sectional area of the wire?
6. If 𝑞(𝑡) = 2𝑡 + 3, what is the electric current at t
5. A total charge of 9.0 mC passes through a crosssectional area of a nichrome
=2s?
a) 1.2 A b)2A c)4A d)10A
wire in 3.5 s.
a. What is the current in the wire?
b. How many electrons pass through the cross-sectional
area in 10.0 s?
8. If I(𝑡) = 3𝑡 2 − 2, how many electrons will
7.In a certain circuit, the current as a function of time is
be flowing from t =1s to t= 2s?
given as: 𝑖(𝑡) = 3𝑡 2 – 2𝑡, where 𝑖 is measured in
milliamps and 𝑡 is measured in seconds. How many
charges passes through this circuit during the interval 0
< 𝑡 < 5.00 𝑠 ?
A. 28.0 mC B. 65.0 mC C. 100 mC D. 150 mC
9. If the given equation between the charge in
10.
The Stanford Linear Accelerator
coulomb and the time in second is 𝑞(𝑡) = 𝑥𝑡 2 + accelerated a beam consisting of 2.0
14
electrons per second through a
2 , When the current is equal to 10 milli-ampere X10
at t=2s. What is the value of x in C/s unit?
𝑑𝑞
potential difference of 2.0 X1010 V.
Calculate the current in the beam.
(𝐼 = 𝑑𝑡 ,
0.01 = 2𝑥𝑡, 𝑜𝑟 𝑥 =
0.01
= 2.5 × 10−3 𝑐/𝑠
2×2
A) 𝟐 × 𝟏𝟎𝟏𝟒 𝑨
c) 𝟏𝟎𝟎𝟎𝟎 𝑨
5.2 current density J
b) 𝟑. 𝟐 × 𝟏𝟎−𝟓 𝑨
d) 𝟒 × 𝟏𝟎𝟐𝟒 𝑨
Formulae:
Current, 𝐼 = 𝑒𝑛𝐴𝑣𝑑 ,
current density: 𝐽 =
If the electric current through the wire is, 𝐼 = 𝑒𝑛𝐴𝑣𝑑 , then
𝐼
current density: 𝐽 = 𝐴 = 𝑒𝑛𝑣𝑑
Where, 𝑣𝑑 is the velocity of the electron in the presence of an
electric field.
𝐼
𝐴
= 𝑒𝑛𝑣𝑑
A = area of cross section of the conductor.
N = number of electrons per unit volume.
The
drift velocity vector is antiparallel to the current density vector.
11.
What is the current density in an 12.
Which is the correct statement about the
aluminum wire having a radius of 1.00 direction of current density?
mm and carrying a current of 1.00 mA? a) It is in the same direction as that of the
a) 318 A/m2
c) 3. 18 A/m2
electron flow.
b) 100 A/m2
d) 1.14 A/m2
b) It is in the opposite direction of the electric
field that causes the flow of the charges.
c) It is from the negative to positive terminal
of the battery.
d) It will be always antiparallel to the drift
velocity vector.
14.
A current with density 300 A/m2 is
flowing through a wire of cross-sectional
13.
What is the current density in an area 3mm2.How many charges will be
aluminum wire if the density of aluminum is passing through this wire after 12s?
2.70 X103 kg/m3 and 1 mole of aluminum has a)10.8mC b) 7.2nC c) 14.5pC d)0.2µC
a mass of 26.98 g. There is one conduction
electron per atom in aluminum. The drift
velocity of the electrons through the wire is
1.4 X 10-8 m/s.(NA=6.023X 1023)
A) 332 A/m2
b)135 A/m2
c) 224 A/m2
d)75A/m2
15.
A current of 0.123 mA flows in a silver 16.
What are the units of current
wire whose cross-sectional area is 0.923 density?
mm2. What is the current density?
0.133A/m2
a)
a)
c)7.5A/m2
b) 133.3A/m2
c)A/m2
C/s
d) V/Ωm2
b) Cm/s
d)7500 A/m2
5.3 Resistance and resistivity
𝑉
Resistance (R)- opposition to the flow of charges.𝑅 = Ohm’s law: 𝐼 = 𝑅
∆𝑉
1
𝐼
I
conductance G, 𝐺 = 𝑅 = 𝛥𝑉
 unit is ohms 𝛺 (=Volt/ampere).
Ohm’s law :- A basic law regarding flow of currents was
discovered by G.S. Ohm in 1828, known as Ohm’s law:
𝑉
𝐼
=𝑅
More the resistance less will be the current .
Resistivity ( 𝜌)- measure of how strongly a material
opposes the flow of charges.
 unit is Ohm-meter(𝛺.m)
 Resistivity for a conductor of length L and area A is,
R𝐴
𝜌= 𝐿.
Resistivity for a conductor of length L and area A
𝛥𝑉
𝐿
𝐸
R𝐴
is, 𝜌 = 𝐿
 Ohm’s law in terms of resistivity, 𝜌 = 𝐽 = 𝐽
Conductance:
Inverse
1
of
resistance
is
called
I
conductance G, 𝐺 = 𝑅 = 𝛥𝑉
1
𝐿
𝐽
Conductivity, 𝜎 = 𝜌 = 𝑅𝐴 = 𝐸
 unit is siemens(S) 1S =1A/1V
conductivity : The inverse of resistivity is called
conductivity, 𝜎 =
1
𝜌
=
𝐿
𝑅𝐴
=
𝐽
𝐸
 Unit of conductivity is Ohm-meter inverse (𝛺. 𝑚)−1
17.
A potential difference of 2.0 𝑉
is
applied across a wire of cross- sectional area
2.5 𝑚 𝑚 2. The current which passes through
18.
Which of the following is true
regarding resistivity and resistance
of a wire?
the wire is 3.2 × 10−3 𝐴 . What is the a) The resistance of the wire is directly
proportional to its cross-sectional area.
resistance of the wire?
b) The resistance of the wire is inversely
2
2
A. 2.8 × 10 𝛺
B. 3.6 × 10 𝛺 proportional to its length.
c) Per unit length and per unit crossC. 4.2 × 102 𝛺
D. 6.3 × 102 𝛺
sectional area for any material the same
resistance.
d) The resistivity of the wire depends
on its material type.
19.
A
1.0
mm
wire
of
diameter of 1.7 mm and length of
resistivity 1.7  10-8 m is connected
1.3 m. If its resistance is 15 m,
across a 3.0 V battery. The current
what is the resistivity of the metal
through the wire is ____.
from which it is made?
diameter
20
cm
thick
long
and
copper
20.
A
particular
A. 7.00 A B. 125 A C. 693 A D. 789 A A. 1.0  10−7 m
21.
wire
has
B. 2.6  10−8 m
C. 4.4  10−6 m
D. 1.8  10−5 m
The resistivity of a conductor is
22.
A potential difference of
ρ = 1.00 X10-5 Ω m. If a cylindrical
12.0 V is applied across a wire of
wire is made of this conductor, with a
cross-sectional area 4.50 mm2 and
cross-sectional area of 1.00 X10-6 m2
length
, what should the length of the wire be
passing through the wire is 3.20 x
for its resistance to be 10.0 Ω?
10-3A.
a)3.2m b) 0.47 m
c) 1m d)12m
1000.
km.
The
current
What is the resistivity of
this wire?
A) 𝟏. 𝟔𝟗 × 𝟏𝟎−𝟖 𝛀𝒎 c) 0.0169 𝛀𝒎
𝐛)𝟖. 𝟑𝟑 × 𝟏𝟎𝟖 𝛀𝒎
.
a
d) 𝟏. 𝟕 × 𝟏𝟎−𝟏𝟏 𝛀𝒎