DP024 FLIPBOOK 2 OF 3 (TOPIC 4-5)

THE GREEK ALPHABET

A  Alpha

B  Beta

  Gamma

  Delta

  Epsilon

  Zeta

  Eta

  Theta

  Iota

  Kappa

  Lambda

  Mu

  Nu.

  Xi

  Omicron

  Pi

  Rho

  Sigma

  Tau

  Upsilon

  ,  Phi

  Chi

  Psi

  Omega

i

LIST OF SELECTED CONSTANT VALUES
SENARAI NILAI PEMALAR TERPILIH

ii

LIST OF SELECTED CONSTANT VALUES
SENARAI NILAI PEMALAR TERPILIH

iii

LIST OF SELECTED FORMULAE
SENARAI RUMUS TERPILIH

1. a    2 x

2. x  A sin t B  o NI
17. 2R
v  dx
3. dt B  o NI
18.  L
a  dv 19.   B  A
4. dt 20. Φ = N
21. ε  Blvsin
5. y(x,t)  A sin(t  kx)

v  dy  NA dB
6. dt

7. v  f 22. ε dt

I  dQ  NB dA
8. dt dt
23. ε
  RA
9. l 24. r  2 f

10. Reff  R1  R2  R3  ... Rn 1 11
25. f u v
1  1  1  1  ... 1
11. Reff R1 R2 R3 Rn m  hi   v
26. ho u
1  1  1  1  ... 1
12. Ceff C1 C2 C3 Cn ym  mD
d
27.

13. Ceff  C1  C2  C3  ... Cn  m  1 D

t ym   2
d
14. Q  Qo e RC 28.

Q  Qo 1 - e t  y  D
RC 29. d

15.

B  oI
16. 2R

iv

TOPIC 4
CAPACITOR
4.1 Capacitance and capacitors in series and parallel
a) Define capacitance,
b) Use capacitance, C  Q .

V
c) Calculate the effective capacitance of various arrangements by

using thefollowing formulae:
Series: 1 = 1 + 1 + 1 +. ..

1 2 3

Parallel: = 1 + 2 + 3+. ..
4.2 Charging and discharging of capacitors

a) State physical meaning of time constant and use  RC .
b) Sketch Q-t and I-t graph for charging and discharging of a capacitor.
c) Explain the characteristics of Q-t and I-t graph for charging and discharging

of a capacitor.
d) Use:

(i) for discharging

−

=
(ii) for charging

−

= (1 − )
e) Determine the time constant of an RC circuit.

(Experiment 4: Capacitor – Determine time constant and capacitance only)

17

OBJECTIVE QUESTIONS

(C2, PLO 1, MQF LOD 1)

1. The unit of capacitance is
A. Farad.
B. Coulomb.
C. Henry.
D. Weber.

2. The effective capacitance of a capacitor is reduced when capacitors are
connected in
A. series.
B. parallel.
C. series-parallel combination.
D. none of the above.

3. Three capacitors each of capacity C are given. The resultant capacity 2 C can

3

obtained by using them
A. all in series.
B. all in parallel.
C. two in parallel and third in series with the combination.
D. two in series and third in parallel across this combination.

4. An initially uncharged parallel plate capacitor of capacitance C is charged to
potential V by a battery. The battery is then disconnected. Which statement is
correct?
A. There is no charge on either plate of the capacitor.
B. The capacitor can be discharged by grounding any one of its two plates.
C. The capacitance increases when the distance between the plates increases.

D. The magnitude of the electric field outside the space between the plates is
approximately zero.

5. When is a capacitor fully charged?
A. When the voltage across its plates is 1 of the voltage from ground from

2

ground to one of its plates.

B. When the current through the capacitor is the same as when the capacitor is
discharged.

C. When the voltage across the plates is 0.707 of the input voltage.

D. When the current through the capacitor is directly proportional to the area of
the plates.

6. You could increase the time constant of an RC circuit by
A. adding a resistor in parallel with the circuit resistance
B. adding a capacitor in parallel with the circuit capacitance
C. increasing the amplitude of the input voltage
D. exchanging the position of the resistor and capacitor in the circuit

ANSWERS:

1. A 2. A 3. B 4. D 5. B 6. B

18

STRUCTURED QUESTIONS

(C3, PLO 4, CTPS 2, MQF LOD 6)

1. (a) Two conductors having net charges of 10.0 C and 10.0 C have a
potential difference of 10.0 V between them. What is the potential difference
between the two conductors if the charge on each conductor is increased to
100 C and 100 C?

(b) When the potential difference between the plates of a capacitor is 3.25 V,
the magnitude of the charge on each plate is 13.5 C. What is the
capacitance of this capacitor?

2. 1 F (b)
(a)
4 F

3 F

a 6 F 3 F b 6 F
2 F
a b

8 F 4 F

2 F

FIGURE 4.1 (a) FIGURE 4.1 (b)

Calculate the effective capacitance between a and b as shown in FIGURE 4.1(a)
and 4.1(b).

a
3. C1 C4

C2 C3 C5

C6 C7

b
FIGURE 4.2
The combination of seven capacitors are arranged as shown in FIGURE 4.2.
Determine the equivalent capacitance between points a and b if C1  C4  5.0 F,
C2  C5  C6  C7  10.0 F and C3  2.0 F.

19

4.
15 F 3 F

20 F
ab

6 F
FIGURE 4.3
Four capacitors are arranged as shown in the FIGURE 4.3. Determine the effective
capacitance between a and b.
5. A 3 F capacitor and a 6 F capacitor, which are initially uncharged, are connected
in series with a 12 V battery. Determine the potential difference across the 6 F
capacitor.
6. Two capacitors, C1  5.0 F and C2  12.0 F, are connected in parallel and the
resulting combination is connected to a 9.0 V battery.
Determine
(a) the equivalent capacitance.
(b) the potential differences across each capacitor.
(c) the charge stored on each capacitor.
7.

V C1
C2 C3

FIGURE 4.4

Three capacitors are arranged as shown in the FIGURE 4.4. If V  12 V,
C1  3 F, C2  2 F and C3  4 F.
Determine
(a) the effective capacitance.
(b) the potential difference across C1.
(c) the charge on the capacitor C2.

20

8. C1 C2
ΔV

S1 S2

FIGURE 4.5

Consider the circuit shown in FIGURE 4.5, where C1 = 6.0 F, C2 = 3.0 F, and ΔV
= 20.0 V. Capacitor C1 is first charged by the closing of switch S1. Switch S1 is then
opened, and the charged capacitor is connected to the uncharged capacitor by the
closing of S2. Calculate the initial charge acquired by C1 and the final charge on
each capacitor.

9. A 300 F capacitor is to be charged by a 12.0 V battery through of 20 k resistor.
(a) What is the time constant of the circuit?
(b) Calculate the maximum charge stored in the capacitor.
(c) Find the time required to reach 50% of the maximum charge.

10. (a) A fully charged capacitor has 12.0 F and 6.0 mC charge. The capacitor has
been discharged through 100  resistors. Determine
(i) the potential difference across the capacitor.
(ii) the time constant for charging circuit.
(iii) the time taken if just 20% charge left in the capacitor.

(b) Sketch I-t graph to show a discharging process of a capacitor.

11. A 6.0 F capacitor, a 5 k resistor and a 12.0 V battery are connected in series. If
the capacitor is initially uncharged, determine,

(a) the initial current in the circuit when the switch is closed.
(b) the time required for the current in the circuit to drop from its initial value to

1.2 mA.

21

ANSWERS:

1. (a) 100 V (b) 4.15 F

2. (a) 6 F (b) 8.5 F

3. 6.04 F

4. 5.95 F

5. 4 V

6. (a) 17 F (b) 9.0 V (c) 4.50×10 C (45 C); 1.08×10 C (108 C)

7. (a) 2 F (b) 8 V (c) 24 C

8. Q2 = 40.0 C; Q1 = 80.0 C

9. (a) 6 s (b) 3.6×10 C (c) 4.16 s

10. (a) (i) 500 V (ii) 1.2 ms (iii) 1.93 ms

11. (a) 2.4×10 A (b) 20.8 ms

22

TOPIC 5
MAGNETISM & ELECTROMAGNETIC INDUCTION

5.1 Magnetism
a) Define magnetic field.
b) Identify magnetic field sources
* Example:
i. Bar magnet and current-carrying conductor (straight wire and circular coil).
ii. Earth magnetic field.

5.2 Magnetic field produced by current-carrying conductor
a) Sketch magnetic field lines patterns of current carrying straight wire, circular coil
and solenoid
b) Calculate the magnetic field by using:
i. for a long straight wire

= 2

ii. at the center of a circular coil


= 2

iii. at the center of solenoid
=


5.3 Magnetic flux
a) Define and use magnetic flux, = ⋅
b) Use magnetic flux linkage, Φ = .

5.4 Induced emf
a) State Faraday’s law
b) Use Faraday’s law
c) State Lenz’s law
d) Use Lenz’s law to find the direction of induced current.
e) Use induced emf in
i. a straight conductor, = sin
ii. a coil,
= − , = −



(Experiment 5 : Magnetic Field : Earth Magnetic Field)

23

OBJECTIVE QUESTIONS

(C2, PLO 1, MQF LOD 1)

1. Which of the following statements is NOT true about a bar magnet?
A. Its magnetic flux is greater at the poles
B. Its magnetic field lines form a closed loop
C. Its magnetic fields lines do not intersect one another
D. Its magnetic field lines leave the South-pole and enter the North-pole

2. The magnetism of the Earth acts approximately as if it originates from a huge bar
magnet within the Earth. Which of the following statements are true?
A. The north magnetic pole of the Earth is located at the Earth's North Pole.
B. The south magnetic pole of the Earth is located at the Earth's South Pole.
C. The Earth's magnetic field is vertical at the equator.
D. The Earths north magnetic pole is magnetically a south pole.

3. The SI unit of magnetic field is the tesla, which is equivalent to a:
A. N C-1
B. A m-1
C. Wb m-2
D. N m-1

4. A metal rod of length (l) moves with velocity (v), perpendicular to its length, in a
magnetic field B, which is perpendicular to both the rod and its velocity. If the length
of the rod is doubled, what happens to the electromotive force in the rod?
A. It stays the same.
B. It doubles.
C. It quadruples.
D. It halves.

5. A conducting rod is sliding on metal rails with velocity (v). A magnetic field B is into
the paper, the separation of the rails is L, and the resistance of the circuit is R. In
what direction in the diagram is the current flowing in the resistor?

A. Up
B. Down
C. up then down
D. down then up

ANSWERS:

1. D 2.D 3. C 4.B 5. A
24

STRUCTURED QUESTIONS

(C3, PLO 4, CTPS 2, MQF LOD 6)

1. (a) State two examples of magnetic field sources
(b) Sketch the magnetic field lines of two examples given in (a)
(c) State two characteristics of the magnetic field lines

2. (a) Sketch the pattern of magnetic field of an upright current-carrying wire

where electric current flows through it
i. vertically upward

ii. vertically downward
(b) Sketch the pattern of magnetic field of both sides and center of a coil when

electric current flows through it in direction of clock wise in ONE diagram.

3. (a) A long straight wire carries a current of 5 A (upward). At what distance from the

wire is the magnetic field due to the current in the wire equal in magnitudeto
strength of earth’s magnetic field of 5.0 × 10−5 T.

(b) A circular coil has 15 turns and a diameter of 45.0 cm. If the magnetic field
strength at the centre of the coil is 8.0 × 10−4 T, find the current flowing in the

coil.

4. (a) A power line carries a current of 95 A along the tops of 8.5 m high

poles. What is the magnitude of the magnetic field produced by this wire at

the ground?

(b) A flat circular coil has 50 turns of diameter 1 m.

i. What is the magnetic field strength produced at the center

of the coil by the current of 2 A.

ii. If this coil is set with its axis horizontal in the magnetic meridian, what

are the maximum and minimum values of the horizontal magnetic field
at its center produced by this current? The earth’s horizontal magnetic
field is 18 μT.

5. y yy

x x 20°
20° z x
(iii)
z z
(i) (ii)

FIGURE 5.1

A coil in FIGURE 5.1 has an area of 15 cm2. A magnetic field with B = 0.16 T exits
in positive x-direction.
(a) Calculate the flux through the coil in each orientation shown.
(b) If a coil is replaced by 50 turns of coils, calculate the flux linkage in each

orientation shown.

25

6. (a) A surface of area 100 mm2 inside a uniform magnetic field of strength
0.50 T. The plane of the coil and the direction of the field make an angle α.
Determine the magnetic flux through the surface if
(i) α = 0°
(ii) α = 60°
(iii) α = 90°

(b) A circular coil of 100 turns and diameter of 2.0 cm is placed in a uniform magnetic
field of strength 100 mT. The plane of the field and the direction of the field
makes an angle of 60°. Determine the magnetic flux linkage through the coil.

7. A square coil of sides 15 cm and 300 turns has a resistance of 3.0 Ω. A uniform
magnetic field is applied perpendicular to the plane of the coil. The magnitude of this
field is increased uniformly from 0 to 0.8 Wb m-2 in a time of 0.8 s. Determine
(a) the magnitude of the induced emf in the coil.
(b) the magnitude of the induced current in the coil.

8.

FIGURE 5.2

A 1.5 m conducting rod rests on metal rail PQ and RS as shown in FIGURE 5.2. The
rod is placed in a uniform magnetic field, B = 3.0 T perpendicular to the plane of the
paper. The rod is pulled to the right at a uniform velocity, v = 3.0 m/s. If the resistance
of PQRS is 5 Ω, determine
(a) the magnitude of the induced emf in the rod.
(b) the magnitude and direction of the induced current in the rod.

9. (a) A coil of diameter 12.0 m is placed in a magnetic field. The
magnitude of this field is changed uniformly from 4.2 T to 6.8 Wb m-2 in a
time of 2.0 s.Calculate the induced electromotive force produced by this coil.

(b) A coil of diameter 1.0 m has 310 turns is placed in a magnetic field. The
magnitude of this field is decreased uniformly as much as 2.8 T in a time of
3.0 s. Calculate the back emf of this coil.

10. A copper coil initially 8.0 m in diameter is placed in a uniform magnetic field of
24.0 Wb m-2 at temperature, T1. In time interval 6 s, the coil is shrink to 4.0 m in
diameter as the surrounding temperature drops to T2 and the resistance of this coil
becomes 4.5 Ω. When the coil shrink, the current flows through the coil increases by
0.2 A. Calculate the current flows in the coil at initial temperature, T1.

26

ANSWERS:

1. DIY

2. DIY

3. (a) 0.02 m (b) 19.1 A
4. (a) 2.2 μT (b) 126 μT, 144 μT, 108 μT

5. (a) 2.4 × 10−4 Wb , 2.26 × 10−4 Wb , 8.21 × 10−5 Wb

(b) 1.2 × 10−2 Wb , 1.13 × 10−2 Wb , 4.11 × 10−3 Wb

6. (a) 0 Wb, 4.33 x 10-5 Wb, 5 x 10-5 Wb (b) 2.72 x 10-3 Wb

7. (a) 6.75 V (b) 2.25 A

8. (a) 13.5 V (b) 2.7 A, DIY

9. (a) −147.03 V (b) 227.24 V

10. 33.3 A

27