UNIT 5. CURRENT AND RESISTANCE
5.1 Electric current: Electric current at a point in a
circuit
is
the
rate
at
which net charge moves
past that point.
Direct
current is current flowing
in a direction that does
not change with time.
The direction of 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
reversed.
is
Adding
more bulbs in series,
decreases
brightness
the
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.
Ms. Anu ZEC, RAK
Formulae
𝒅𝑸
𝒏𝒆
𝑰 = 𝒅𝒕 = 𝒕
Unit is Ampere or C/s.
1 A = 1C/1s
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 filament
of the bulb?
3. In a particular television tube, the
beam current is 60.0 µA. How long does
it take for 3.75 × 1014 electrons to strike
the screen?
5. A total charge of 9.0 mC passes
through a cross-sectional area of a
nichrome
2. A 100.0 W light bulb draws 0.83 A
of current. How long does it take for
1.9 × 1022 electrons to pass a given
cross-sectional area of the filament?
4. If a metal wire carries a current of
80.0 mA, how 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 =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?
7. In a certain circuit, the current as a
function of time is given as: 𝑖(𝑡) =
3𝑡 2 – 2𝑡,
where
𝑖
is
measured
8. If I(𝑡) = 3𝑡 2 − 2, how many electrons
will be flowing from t =1s to t= 2s?
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 coulomb and the time in
second
is
Ms. Anu ZEC, RAK
𝑞(𝑡) = 𝑥𝑡 2 + 2
,
When
the
10.
The Stanford Linear Accelerator
accelerated a beam consisting of 2.0
X1014 electrons per second through a
current is equal to 10 milli-ampere at potential difference of 2.0 X1010 V.
t=2s. What is the value of x in C/s unit? Calculate the current in the beam.
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 ,
𝐼
current density: 𝐽 = 𝐴 = 𝑒𝑛𝑣𝑑
If the electric current through the wire is, 𝐼 = A = area of cross section of the
𝐼
conductor.
𝑒𝑛𝐴𝑣𝑑 , then current density: 𝐽 = 𝐴 = 𝑒𝑛𝑣𝑑
Where, 𝑣𝑑 is the velocity of the electron in the
presence of an electric field.
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.
Ms. Anu ZEC, RAK
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?
a)
0.133A/m2
b) 133.3A/m2
c)7.5A/m2
Resistance (R)- opposition to the flow of
∆𝑉
charges.𝑅 = 𝐼
unit is ohms 𝛺 (=Volt/ampere).
Ms. Anu ZEC, RAK
c)A/m2
C/s
b) Cm/s
d) V/Ωm2
d)7500 A/m2
5.3 Resistance and resistivity
➢
a)
𝑉
Ohm’s law: 𝐼 = 𝑅
Ohm’s law :- A basic law regarding flow
of currents was discovered by G.S. Ohm
1
I
conductance G, 𝐺 = 𝑅 = 𝛥𝑉
𝑉
in 1828, known as Ohm’s law: 𝐼 = 𝑅
More the resistance less will be the
current .
Resistivity
(
measure
𝜌)-
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, 𝜌 =
R𝐴
𝐿
.
Resistivity for a conductor of length
➢ Ohm’s law in terms of resistivity, 𝜌 = L and area A is, 𝜌 = R𝐴
𝐿
𝐸
𝛥𝑉
= 𝐽𝐿
𝐽
1
Conductance: Inverse of resistance is
1
𝐿
𝐽
Conductivity, 𝜎 = 𝜌 = 𝑅𝐴 = 𝐸
I
called conductance G, 𝐺 = 𝑅 = 𝛥𝑉
➢
unit is siemens(S) 1S =1A/1V
conductivity : The inverse of resistivity
1
𝐿
𝐽
is called conductivity, 𝜎 = 𝜌 = 𝑅𝐴 = 𝐸
• Unit of conductivity is Ohm-meter
inverse (𝛺. 𝑚)−1
17.
A potential difference of 2.0 𝑉 is 18. Which of the following is true
regarding resistivity and resistance of a
applied across a wire of cross- sectional area
wire?
2.5 𝑚𝑚2. The current which passes through a) The resistance of the wire is directly
proportional to its cross-sectional area.
the wire is 3.2 × 10−3 𝐴. What is the
b) The resistance of the wire is inversely
resistance of the wire?
proportional to its length.
c) Per unit length and per unit crosssectional area for any material the same
resistance.
Ms. Anu ZEC, RAK
A. 2.8 × 102 𝛺
C. 4.2 × 102 𝛺
19.
B. 3.6 × 102 𝛺 d) The resistivity of the wire depends on
D. 6.3 × 102 𝛺
its material type
A 20 cm long and 1.0 mm diameter 20.
A particular wire has a diameter of
thick copper wire of resistivity 1.7  10-8 m 1.7 mm and length of 1.3 m. If its
is connected across a 3.0 V battery. The resistance
is
15
m,
what
is
the
current through the wire is ____.
resistivity of the metal from which it is
A. 7.00 A B. 125 A C. 693 A D. 789 A
made?
A. 1.0  10−7 m
21.
B. 2.6  10−8 m
C. 4.4  10−6 m
D. 1.8  10−5 m
The resistivity of a conductor is ρ = 22. A potential difference of 12.0 V is
1.00 X10-5 Ω m. If a cylindrical wire is made applied across a wire of cross-sectional
of this conductor, with a cross-sectional area area 4.50 mm2 and length 1000. km. The
of 1.00 X10-6 m2 , what should the length of current passing through the wire is 3.20
the wire be for its resistance to be 10.0 Ω? x 10-3A. What is the resistivity of this
a)3.2m b) 0.47 m
c) 1m d)12m
wire?
A) 𝟏. 𝟔𝟗 × 𝟏𝟎−𝟖 𝛀𝒎 c) 0.0169 𝛀𝒎
𝐛)𝟖. 𝟑𝟑 × 𝟏𝟎𝟖 𝛀𝒎
.
Ms. Anu ZEC, RAK
d) 𝟏. 𝟕 × 𝟏𝟎−𝟏𝟏 𝛀𝒎