Upload
jemwesley
View
170
Download
0
Embed Size (px)
Citation preview
Physics Module Form 5 Chapter 2- Electricity GCKL 2011
2-1
CHARGE AND ELECTRIC CURRENT
Van de Graaf
1. What is a Van de Graaff generator? Fill in each of the boxes the name of the part shown.
A device that produces and store electric charges at high voltage on its dome
2. You will feel a brief electric shock when your finger is brought close to the dome of the
generator.
(A) EXPLANATION
i. When the motor of the Van de Graaff generator is switched on, it drives the rubber belt. This
causes the rubber belt to rub against the roller and hence becomes charged. The charge is
then carried by the moving belt up to the metal dome where it is collected. A large amount of
charge is built up on the dome.
ii. The electric field around the metal dome of the generator can produced a strong force of
___________ between the opposite charges. ___________ will suddenly accelerate from the
finger to the dome of the generator and causes a spark.
2.1
dome
rubber belt
Metal dome
roller
roller
motor
+ + +
+
+
+
+ +
+
+
Physics Module Form 5 Chapter 2- Electricity GCKL 2011
2-2
iii. When the wire touches the dome, the microammeter needle is deflected. This shows that a
electric current is flowing through the galvanometer.
iv. The electric current is produced by the flow of charges from earth through the galvanometer
to the metal dome to neutralize the positive charges on its surface.
v. The metal dome can be safely touched with the finger as all the positive charges on it have
been ________________.
3. What will happen if the charged dome of
the Van de Graaff is connected to the
earth via a microammeter? Explain.
There is a deflection of the pointer of the
meter.
This indicates an electric current flow.
The microammeter needle is returned
to its __________________position when the
Van de Graaf is switched off.
2. Predict what will happen if a discharging metal
sphere to the charged dome.
When the discharging metal sphere is
brought near the charged dome, sparkling
occurs.
An electric current flow.
4. The flow of electrical charges produces electric current.
+ + +
+ +
+ +
+
+
+ + + +
+
Physics Module Form 5 Chapter 2- Electricity GCKL 2011
2-3
Electric Current
1. Electric current is defined as the rate of flow of electric charge
2. In symbols, it is given as:
where I = electric current
Q = charge
t = time
(i) The SI unit of charge is (Ampere / Coulomb / Volt)
(ii) The SI unit of time is (minute / second / hour)
(iii) The SI unit of current is (Ampere / Coulomb / Volt) is equivalent to
(Cs // C-1
s // Cs-1
)
(iv) By rearranging the above formula, Q = ( It / t
I / I
t )
3. 1 Coulomb (C) = 1 Ampere Second (As)
4. Example :
Charge of 1 electron = -1.6 × 10-19
C
Charge of 1 proton = +1.6 × 10-19
C
5. Total Charge :
I = Q
t
Physics Module Form 5 Chapter 2- Electricity GCKL 2011
2-4
Electric Field
a) An electric field is a region in which an electric charge experiences a force.
b) An electric field can be represented by a number of lines indicate both the magnitude and
direction of the field
c) The principles involved in drawing electric field lines are :
(i) electric field lines always extend from a positively-charged object to a
negatively-charged object to infinity, or from infinity to a negatively-charged object,
(ii) electric field lines never cross each other,
(iii) electric field lines are closer in a stronger electric field.
EFFECT OF AN ELECTRIC FIELD ON A PING PONG BALL
(a)
(b)
(c)
Observation:
(a) The ball will still remain stationary. This is
because the force exert on the ball by the
positive plate is equal to the force exerted on it
by the negative plate.
(b) If the ping pong ball is displaced to the right
to touch the positive plate, it will then be
charged with positive charge and will be pushed
towards the negative plate.
(c) When the ping pong ball touches the
negative plate, it will be charged with negative
charge and will be pushed towards the positive
plate. This process repeats again and again,
causes the ping pong ball oscillates to and fro
continuously between the two plates.
Physics Module Form 5 Chapter 2- Electricity GCKL 2011
2-5
Conclusion
1. Electric field is a region where an electric charge experiences a force.
2. Like charges repel each other but opposite charges attract each other.
3. Electric field lines are lines of force in an electric field. The direction of the field lines is
from positive to negative.
EXERCISE 2.1
1. 5 C of charge flows through a wire in 10 s. What is the current in the wire?
2. A charge of 300 C flow through a bulb in every 2 minutes. What is the electric current in the
bulb?
3. The current in a lamp is 0.2 A. Calculate the amount of electric charge that passes through
the lamp in 1 hour.
4. If a current of 0.8 A flows in a wire, how many electrons pass through the wire in one
minute? (Given: The charge on an electron is 1.6 x 10-19
C)
Q = It
I = Q/t
= 5 / 10
= 0.5 A
Q = It
I = Q/t
= 300 / 120
= 2.5 A
Q = It
= 0.2 (60 x 60)
= 720 C
Q = It
= 0.8 (60) Convert: 1 minute = 60s
= 48 C
1.6 x 10 -19
C of charge 1 electron.
Hence, 2880 C of charges is brought by
= 3 x 10
20 electrons
Physics Module Form 5 Chapter 2- Electricity GCKL 2011
2-6
An electric current of 200 mA flows through a resistor for 3 seconds, what is the
(a) electric charge
(b) the number of electrons which flow through the resistor?
IDEAS OF POTENTIAL DIFFERENCE
(a)
(b)
Pressure at point P is greater than the
pressure at point Q
Water will flow from P to Q when the
valve is opened.
This due to the difference in the pressure of
water
Gravitational potential energy at X is greater
than the gravitational potential energy at Y.
The apple will fall from X to Y when the apple
is released.
This due to the difference in the gravitational
potential energy.
(a) Q = It
= 200 x 10-3
(3)
= 0.6 C
(b) 1.6 x 10 -19
C of charge 1 electron.
Hence, 2880 C of charges is
= 3.75 x 10
18 electrons
P Q
X
Y
2.2
Physics Module Form 5 Chapter 2- Electricity GCKL 2011
2-7
(c) Similarly,
Point A is connected to positive terminal
Point B is connected to negative terminal
Electric potential at A is greater than the electric
potential at B.
Electric current flows from A to B, passing the bulb in
the circuit and lights up the bulb.
This is due to the electric potential difference between
the two terminals.
As the charges flow from A to B, work is done when
electrical energy is transformed to light and heat energy.
The potential difference, V between two points in a
circuit is defined as the amount of work done, W when
one coulomb of charge passes from one point to the
other point in an electric field.
The potential difference,V between the two points will
be given by:
where W is work or energy in Joule (J)
Q is charge in Coulomb (C)
A B
Bulb
V = echQuantityof
Work
arg = Q
W
Physics Module Form 5 Chapter 2- Electricity GCKL 2011
2-8
EXPERIMENT 1: TO INVESTIGATE THE RELATIONSHIP BETWEEN CURRENT
AND POTENTIAL DIFFERENCE FOR AN OHMIC CONDUCTOR.
(a) (b)
Figure (a) and figure (b) show two electrical circuits. Why do the ammeters show different readings?
Why do the bulbs light up with different intensity?
Referring to the figure (a) and (b) complete the following table:
(a) Inference The current flowing through the bulb is influenced by the potential difference
across it. (b) Hypothesis The higher the current flows through a wire, the higher the potential difference
across it. (c) Aim To determine the relationship between current and potential difference for a
constantan wire.
(d) Variables
(i) manipulated variable
(ii) responding variable
(iii) fixed variable
: current, I
: potential difference, V
: length of the wire // cross sectional area //
temperature
Apparatus /
materials
Physics Module Form 5 Chapter 2- Electricity GCKL 2011
2-9
Method :
1. Set up the apparatus as shown in the figure.
2. Turn on the switch and adjust the rheostat so that the ammeter reads
the current, I= 0.2 A.
3. Read and record the potential difference, V across the wire.
4. Repeat steps 2 and 3 for I = 0.3 A, 0.4 A, 0.5 A, 0.6 A and 0.7 A.
Tabulation of
data
:
Current,I/A Volt, V/V
0.2 1.0
0.3 1.5
0.4 2.0
0.5 2.5
0.6 3.0
0.7 3.5
Analysis of
data
: Draw a graph of V against I
Potential difference, V /V
Current, I /A
3.0 -
2.0 -
1.0 -
0.2 0.4 0.6 0.8
4.0 -
Physics Module Form 5 Chapter 2- Electricity GCKL 2011
2-10
Discussion : 1. From the graph plotted.
(a) What is the shape of the V-I graph?
The graph of V against I is a straight line that passes through origin
(b) What is the relationship between V and I?
This shows that the potential difference, V is directly proportional to
the current, I.
(c) Does the gradient change as the current increases?
The gradient ≡ the ratio of I
V is a constant as current increases.
2. The resistance, R, of the constantan wire used in the experiment is equal
to the gradient of the V-I graph. Determine the value of R.
7.
5.3
o= 5
3. What is the function of the rheostat in the circuit?
It is to control the current flow in the circuit
Conclusion : The potential difference, V across a conductor increases when the current, I
passing through it increases as long as the conductor is kept at constant
temperature.
Ohm’s Law
(a)
Ohm’s law states
that the electric current, I flowing through a conductor is directly proportional to the
potential difference across the ends of the conductor,
if temperature and other physical conditions remain constant
(b) By Ohm’s law: V I
I
V= constant
Physics Module Form 5 Chapter 2- Electricity GCKL 2011
2-11
(c) The constant is known as resistance, R of the conductor.
(d) The unit of resistance is volt per ampere (V A-1
) or ohm ()
Factors Affecting Resistance
1. The resistance of a conductor is a measure of the ability of the conductor to (resist / allow) the
flow of an electric current through it.
2. From the formula V = IR, the current I is (directly / inversely) proportional to the resistance,
R.
3. Write down the relevant hypothesis for the factors affecting the resistance in the table below.
4. From, the following can be stated:
Hence, resistance of a conductor, R
Factors Diagram Hypothesis Graph
Len
gth
of
the
con
du
cto
r, l
The longer the conductor, the
higher its resistance
Resistance is directly proportional
to the length of a conductor
Th
e cr
oss
-sec
tio
nal
area
of
the
con
du
cto
r, A
The bigger the cross-sectional
area, the lower the its resistance
Resistance is inversely
proportional to the cross-
sectional area of a conductor
Th
e ty
pe
of
the
mat
eria
l o
f th
e
con
du
cto
r
Different conductors with the
same physical conditions have
different resistance
Th
e te
mp
erat
ure
of
the
con
du
cto
r
The higher temperature of
conductor, the higher the
resistance
length
cross-sectional area
Physics Module Form 5 Chapter 2- Electricity GCKL 2011
2-12
So R or R = where = resistivity of the
substance
5. i) Electric charge, Q = ( It / t
I /
I
t )
ii) Work done, W = (QV / Q
V /
V
Q )
iii) Base on your answer in 2(i) and (ii) derive the work done, W in terms of I, V and t.
W = QV
= ItV
EXERCISE 2.2
1. If a charge of 5.0 C flows through a wire and the amount of electrical energy converted into heat
is 2.5 J. Calculate the potential differences across the ends of the wire.
W = QV
2.5 = 5.0 (V)
V = 0.5 Volt
2. A light bulb is switched on for a period of time. In that period of time, 5 C of charges passed
through it and 25 J of electrical energy is converted to light and heat energy. What is the potential
difference across the bulb?
W = QV
25 = 5 (V)
V = 5 Volt
3. The potential difference of 10 V is used to operate an electric motor. How much work is done in
moving 3 C of electric charge through the motor?
W = QV
= 3 (10)
= 30 J
l
A
l
A
Physics Module Form 5 Chapter 2- Electricity GCKL 2011
2-13
4. When the potential difference across a bulb is 20 V,
the current flow is 3 A. How much work done to
transform electrical energy to light and heat energy
in 50 s?
W = VIt
= 20 (3) (50)
= 3000 J
5. What is the potential difference across a light bulb of resistance 5 when the current that passes
through it is 0.5 A?
V = IR
= 0.5 (5)
= 2.5 V
6. What is the value of the resistor in the figure, if the dry
cells supply 2.0 V and the ammeter reading is 0.5 A?
V = IR
2.0 = 0.5 (R)
R = 4
7. If the bulb in the figure has a resistance of 6 , what is
the reading shown on the ammeter, if the dry cells
supply 3 V?
V = IR
3.0 = 6 (I)
I = 0.5 A
8. If a current of 0.5 A flows through the resistor of 3
in the figure, calculate the voltage supplied by the dry
cells?
V = IR
= 0.5 (3)
V = 1.5 V
3 A
A 20 V
Bulb
Physics Module Form 5 Chapter 2- Electricity GCKL 2011
2-14
9. Referring to the diagram on the right, calculate
(a) The current flowing through the resistor.
V = IR
12 = I (5)
I = 2.4 A
(b) The amount of electric charge that passes through
the resistor in 30 s
Q = It
= 2.4 (30)
= 72 C
(c) The amount of work done to transform the electric
energy to the heat energy in 30 s.
W = QV or W = VIt
= 72 (12) = 12(2.4)(30)
= 864 J = 864 J
10. The graph shows the relationship between the
potential difference, V and current, I flowing
through two conductors, X and Y.
a) Calculate the resistance of conductor X.
From V-I graph, resistance = gradient
=2
8
= 4
b) Calculate the resistance of conductor Y.
From V-I graph, resistance = gradient
=2
2
= 1
c) If the cross sectional area of X is 5.0 x 10-6
m2, and the length of X is 1.2 m, calculate its
resistivity.
I/A
V/V
0 0
X
Y
2
8
2
12 V
5 I
R = A
l
ρ = l
RA
=2.1
)10x0.5(4 6
= 1.67 x 10-5m
I
Physics Module Form 5 Chapter 2- Electricity GCKL 2011
2-15
SERIES AND PARALLEL CIRCUITS
Current Flow and Potential Difference in Series and Parallel Circuit
SERIES CIRCUIT PARALLEL CIRCUIT
1. Effective Resistance:
R =
2. Current:
3. Potential Difference:
V =
1. Effective Resistance:
R =
2. Current:
3. Potential Difference:
V =
Effective resistance, R
(a) R = 20 + 10 + 5= 35
(b) 1/R = ½ +1/5 + 1/10 = 4/5
Effective R = 1.25
2.3
Physics Module Form 5 Chapter 2- Electricity GCKL 2011
2-16
(c) 1/R = 1/8 + 1/8= 1/4
R = 4
Effective R = 20 + 10 + 4 = 34
(d) 1/R =1/16 + 1/8 + 1/8
=5/16
Effective R = 3.2
(e) 1/R = 1/4 + 1/2=3/4
R = 1.33
Effective R = 1.33 + 1 = 2.33
(f) 1/R = 1/4 + 1/12=1/3
R = 3
Effective R = 3 + 2 = 5
(g) Effective R = 2+5+3+10
= 20
(h) 1/R = 1/20 + 1/20=1/10
R = 10
Effective R = 10 + 10 + 5 =2 5
EXERCISE 2.3
1. The two bulbs in the figure have a resistance of 2 and 3
respectively. If the voltage of the dry cell is 2.5 V, calculate
(a) the effective resistance, R of the circuit
Effective R = 2 + 3 = 5
(b) the main current, I in the circuit (c) the potential difference across each bulb.
V = IR 2: V = IR = (0.5)(2) = 1V
2.5 =I(5) 3: V = IR = (0.5)(3) = 1.5 V
= 0.5 A
Physics Module Form 5 Chapter 2- Electricity GCKL 2011
2-17
2.
There are two resistors in the circuit shown. Resistor R1 has a
resistance of 1. If a 3V voltage causes a current of 0.5A to flow
through the circuit, calculate the resistance of R2.
V = IR
3=0.5(1+R2)
R2 = 5
3.
The electrical current flowing through each branch, I1 and I2, is 5
A. Both bulbs have the same resistance, which is 2. Calculate
the voltage supplied.
Parallelcircuit;V =V1=V2 = IR1 or
= IR2
= 5(2)
= 10 V
4. The voltage supplied to the parallel is 3 V. R1 and R2
have a resistance of 5 and 20. Calculate
(a) the potential difference across each resistor
3 V (parallel circuit)
(b) the effective resistance, R of the circuit
1/R = 1/5 + 1/20 =1/4
R = 4
(c) the main current, I in the circuit (d) the current passing through each resistor
V = IR 5: V = IR 20 : V = IR
3 =I(4) 3 =I(5) 3 =I(20)
I = 0.75 A I = 0.6 A I = 0.15 A
Physics Module Form 5 Chapter 2- Electricity GCKL 2011
2-18
ELECTROMOTIVE FORCE AND
INTERNAL RESISTANCE
Electromotive force
Figure (a) Figure (b)
1. An electrical circuit is set up as shown in figure (a). A high resistance voltmeter is connected
across a dry cell which labeled 1.5 V.
a) Figure (a) is (an open circuit / a closed circuit)
b) There is (current flowing / no current flowing) in the circuit. The bulb (does not light up / lights
up)
c) The voltmeter reading shows the (amount of current flow across the dry cell / potential difference
across the dry cell)
No current flow
R
Voltmeter reading,
e.m.f.
Voltmeter reading,
potential difference, V < e.m.f., E
E , r
Current flowing
2.4
Physics Module Form 5 Chapter 2- Electricity GCKL 2011
2-19
2. The switch is then closed as shown in figure (b).
a) Figure (b) is (an open circuit / a closed circuit)
b) There is (current flowing / no current flowing) in the circuit. The bulb (does not light up / lights
up)
c) The voltmeter reading is the (potential difference across the dry cell / potential difference across
the bulb / electromotive force).
d) The reading of the voltmeter when the switch is closed is (lower than/ the same as / higher than)
when the switch is open.
e) State the relationship between e.m.f , E , potential difference across the bulb, VR and drop in
potential difference due to internal resistance, Vr.
Electromotive force, e.m.f., E = Potential Difference + Drop in Potential Difference
across resistor, R due to internal resistance,r
= VR + Vr where VR = IR and Vr = Ir
= IR + Ir
= I (R + r)
3.
a) Why is the potential difference across the resistor not the same as the e.m.f. of the battery?
The potential drops as much as 0.4 V across the internal resistance
b) Determine the value of the internal resistance.
Since E = V + Ir
1.5 = 1.1 + 0.5 r
r = 0.8
Therefore, the value of the internal resistance is 0.8
Physics Module Form 5 Chapter 2- Electricity GCKL 2011
2-20
EXERCISE 2.4
1
A voltmeter connected directly across a battery gives a reading of
1.5 V. The voltmeter reading drops to 1.35 V when a bulb is
connected to the battery and the ammeter reading is 0.3 A. Find the
internal resistance of the battery.
E = 3.0 V, V = 1.35 V, I = 0.3 A
Substitute in : E = V + Ir
1.5 = 1.35 + 0.3(r)
r = 0.5
2. A circuit contains a cell of e.m.f 3.0 V and internal resistance, r. If the external resistor has a
value of 10.0 and the potential difference across it is 2.5 V, find the value of the current, I in the
circuit and the internal resistance, r.
E = 3.0 V, R = 10 , V = 2.5 V
Calculate current : V = IR
Calculate internal resistance : E = I(R + r)
r = 2.0
3 A simple circuit consisting of a 2 V dry cell with an internal resistance of 0.5. When the
switch is closed, the ammeter reading is 0.4 A.
Calculate
(a) the voltmeter reading in open circuit
The voltmeter reading = e.m.f. = 2 V
(b) the resistance, R (c) the voltmeter reading in closed circuit
E = I(R + r) V = IR
2 = 0.4(R + 0.5) = 0.4 (4.5)
R = 4.5 = 1.8 V
Physics Module Form 5 Chapter 2- Electricity GCKL 2011
2-21
4
Find the voltmeter reading and the resistance, R of the
resistor.
E = V + Ir
12 = V + 0.5 (1.2)
V = 11.4 V
V = IR
11.4 = 0.5 (R)
R = 22.8
5
A cell of e.m.f., E and internal resistor, r is connected to a rheostat. The ammeter reading, I and
the voltmeter reading, V are recorded for different resistance, R of the rheostat. The graph of V
against I is as shown.
From the graph, determine
a) the electromotive force, e.m.f., E b) the internal resistor, r of the cell
E = V + Ir r = - gradient
Rearrange : V = E - I r = - (6 - 2)
Equivalent : y = mx + c 2
Hence, from V – I graph : E = c = intercept of V-axis = 2
= 6 V
e.m.f.
6
2
2 /A
/ V
Physics Module Form 5 Chapter 2- Electricity GCKL 2011
2-22
ELECTRICAL ENERGY AND POWER
Electrical Energy
Electrical Energy and Electrical Power
1. Potential difference, V across two points is the energy,E dissipated or transferred by a
coulomb of charge, Q that moves across the two points.
2. Therefore,
3. Hence,
4. Power is defined as the rate of energy dissipated or transferred.
5. Hence,
Electrical Energy, E Electrical Power, P
From the definition of
potential difference, V
Power is the rate of transfer of electrical
energy,
Electrical energy converted, E
; where Q = It
Hence,
; where V = IR
Hence,
; where I = V
R
SI unit : Joule (J)
SI unit : Joule per second // J s-1
// Watt(W)
E Q
V =
E = VQ
E = VI t
E t
P =
VQ t
P =
P = VI
I2 R
P =
Electrical energy dissipated, E
Charge, Q
Potential difference, V =
E = VQ
Energy dissipated, E
time, t
Power, P =
2.5
V2 t
R E =
Physics Module Form 5 Chapter 2- Electricity GCKL 2011
2-23
Power Rating and Energy Consumption of Various Electrical Appliances
1. The amount of electrical energy consumed in a given period of time can be calculated by
Energy consumed = Power rating x Time
E = Pt where energy, E is in Joules
power, P is in watts
time, t is in seconds
EXAMPLE:
1. COST OF ENERGY
Appliance Quantity Power / W Power / kW Time
Energy
Consumed
(kWh)
Bulb 5 60 0.3 8 hours 2.40
Refrigerator 1 400 0.4 24 hours 9.6
Kettle 1 1500 1.5 3 hours 4.5
Iron 1 1000 1.0 2 hours 2
Total energy consumed, E = (2.40 + 9.6 + 4.5 + 2.0)
= 18.50 kWh
Cost = 18.50 kWh x RM 0.28
= RM 5.18
Physics Module Form 5 Chapter 2- Electricity GCKL 2011
2-24
EXERCISE 2.5
1. How much power dissipated in the bulb?
(a)
(b)
2.
Calculate
(a) the current, I in the circuit (b) the energy released in R 1 in 10 s.
(b) the electrical energy supplied by the battery in 10 s.
5 V
R = 10
5 V
R = 10
R = 10
R1=2 R2=4 R3=4
V= 15V I
P = V2
R
= 52 / 10
= 2.5 W
P = V2
R
= 52 / 5
= 5 W
Total resistance, R = (2 + 4 + 4)
= 10
V = IR
I = V/R
= 15 / 10
= 1.5 A
E = I2Rt
= (1.5)2 (10)(10)
= 225 J
E = I2Rt
= (1.5)2 (2)(10)
= 45 J
Physics Module Form 5 Chapter 2- Electricity GCKL 2011
2-25
3. An electric motor is used to lift a load of mass 2 kg to a height 5 m in 2.5 s. If the supply voltage is
12 V and the flow of current in the motor is 5.0 A, calculate
(a) Energy input to the motor
(b) Useful energy output of the motor
(c) Efficiency of the motor
E = VIt
= 12 (5.0) (2.5)
= 150 J
U = mgh
= 2 (9.8) (5)
= 98 J
Efficiency = Output power x 100 %
Input power
= 98 x 100 %
150
= 65.3 %
Physics Module Form 5 Chapter 2- Electricity GCKL 2011
2-26
REINFORCEMENT EXERCISE CHAPTER 2
Part A: Objective Questions
1. Which of the following diagrams shows
the correct electric field?
2.
Diagram1show a lamp connected to a
resistor and a battery.
Calculate the power used by the light bulb.
A 6 W
B 12 W
C 20 W
D 50 W
3. When the switch is on, the current that
flows in an electronic advertisement board
is 3.0 x 10 -5
A. What is the number of
electrons flowing in the advertisement
board when it is switched on for 2 hours ?
[ Charge of an electron = 1.6 x 10 -19
C ]
A 3.84 x 1011
B 1.67 x 1014
C 1.35 x 1018
4. A current of 5 A flows through an
electric heater when it is connected to the 240
V main supply. How much heat is released
after 2 minutes?
A 1 200 J
B 2 400 J
C 14 400 J
D 144 000 J
5. An electric bulb is labeled “240V,
60W”. How much energy is used by
the bulb in one minute if the bulb is
connected to a 240V power supply?
A 60 J
B 360 J
C 600 J
D 3600 J
6. The diagram shows a cell of negligible
internal resistance connected to two
resistors
What is the value of current, I?
A 0.45 A
B 0.40 A
C 0.25 A
Diagram 1