Note Physics 2 SP025

Resonance in RCL series circuit
Figure below shows the variation of XC, XL, R and Z with
frequency f of the RCL series circuit.

47

The value of impedance is minimum Zmin when

where its value is given by

This phenomenon occurs at the frequency fr known as

resonant frequency.

48

At resonance in the RCL series circuit, the impedance is
minimum Zmin thus the rms current flows in the circuit is

maximum.
At frequencies above or below the resonant frequency

fr, the rms current I is less than the rms maximum

current.

49

The resonant frequency, fr of the RCL series circuit

is given by

and

Note: where

At resonance, the current I and voltage V are in phase.

The series resonance circuit is used for tuning a radio receiver. 50

EXAMPLE QUESTION 7

Find the impedance of a series RLC circuit if the inductive reactance, capacitive
reactance and resistance are 184 Ω, 144 Ω and 30 Ω respectively. Also calculate the
phase angle between voltage and current.

ANSWER

(Answer: 50 Ω; 53.1) 51

EXAMPLE QUESTION 8

A 500 μH inductor, 80/π2 pF capacitor and a 628 Ω resistor are connected to form a
series RLC circuit. Calculate the resonant frequency.

ANSWER

(Answer: 2500 kHz) 52

6.4 Power and Power Factor

Average Power ( Pav )
Also known as Real power

There are no power dissipated in capacitor (C) & inductor
(L). Capacitor & inductor absorb power on the first quarter
and return to the AC generator on the next quarter-cycle.
The ONLY power dissipation takes place in resistor (R).

The average power (or real power) dissipated in a RC, RL or
RCL series circuit :

(1)

Note : I and V in equation refer to rms values.

53

From the phasor diagram of the RCL series circuit :

We get
then the eq. (1) can be written as

and

54

where cos φ is called the power factor of the AC circuit,
Pr is the average real power and I2Z is called the
apparent power.
Power factor is defined as

where
From the phasor diagram, power factor also can be calculated
by using the equation below:

55

Instantaneous power, P

Is defined as the product of the instantaneous current, and
voltage, .

Pure resistor
Pure capacitor
Pure inductor

56

EXAMPLE QUESTION 9

A capacitor of capacitance 10-4 /π F, an inductor of inductance 2/ π H and a
resistor of resistance 100 Ω are connected to form a series RLC circuit.
When an AC supply of 220 V, 50 Hz is applied to the circuit, determine
the power factor of the circuit and the power factor of the circuit at
resonance.

ANSWER

(Answer: 0.707; 1) 57

EXAMPLE QUESTION 10

Sketch the graph of instantaneous power P of the pure Inductor against time t.
Explain on the signficant of the variation of power againts time

ANSWER

(Answer: refer to the video Chapter 6-6.4) 58

Next topic …

TOPIC 7
GEOMETRICAL OPTICS

60

TOPIC 7 :
GEOMETRICAL OPTICS

7.1 Reflection at a spherical surface
7.2 Refraction at a spherical surface
7.3 Thin lens

MODE Face to face SLT Non Face to face SLT

Lecture 1 1
Tutorial
8 8
Practical (2 for pre & post lab) (2 for pre & post lab)

2 none

Learning outcomes

At the end of this topic, students should be able to:

7.1 Reflection at a spherical surface

a) State radius of curvature, R= 2f for spherical mirror.

(Lecture : C1,CLO1, PLO1, MQF LOD1)

b) Sketch ray diagram with a minimum of two rays to
determine the characteristics of image formed by
spherical mirrors. (Tutorial : C3, CLO3,PLO4, CTPS3, MQF LOD6)

c) Use mirror equation, = + for real object only.

* Sign convention for focal length, f

i. Positive f for concave mirror

7.3 ii. Negative f for convex mirror

(Tutorial : C3, CLO3,PLO4, CTPS3, MQF LOD6)

d) Define and use magnification, = = −

respectively
(Lecture : C1,CLO1, PLO1, MQF LOD1)

(Tutorial : C3, CLO3,PLO4, CTPS3, MQF LOD6)

Learning outcomes

At the end of this topic, students should be able to:

7.2 Refraction at a spherical surface

a) Use for spherical surface

* sign convention for radius of curvature, R
i. Positive R for convex surface
ii. Negative R for concave surface

(Tutorial : C3, CLO3,PLO4, CTPS3, MQF LOD6)

Learning outcomes

At the end of this topic, students should be able to:

7.3 Thin Lenses

a) Sketch ray diagrams with a minimum of two
rays to determine the characteristics of image
formed by concave and convex lenses.

(Tutorial : C3, CLO3,PLO4, CTPS3, MQF LOD6)

b) Use thin lens equation, = + for real object only.

* sign convention for focal length, f
i. Positive f for convex lens
ii. Negative f for concave lens

(Tutorial : C3, CLO3,PLO4, CTPS3, MQF LOD6)

c) Determine the focal length of a convex lens
(Experiment 5: Geometrical Optics)

Learning outcomes

At the end of this topic, students should be able to:

7.3 Thin Lens

d) State and use lens maker’s equation,

1 11
= − 1 −

∗ = 1 (Lecture : C1,CLO1, PLO1, MQF LOD1)
(Tutorial : C3, CLO3,PLO4, CTPS3, MQF LOD6)

e) Define and use magnification, = = −

respectively
(Lecture : C1,CLO1, PLO1, MQF LOD1)

(Tutorial : C3, CLO3,PLO4, CTPS3, MQF LOD6)

RECALL PRIOR KNOWLEDGE

o Reflection is defined as the return of all or part of a beam of
light when it encounters the boundary between two media.

The incident ray, the reflected ray &
the normal all lie in the same plane.

Angle of reflection, r equals the

angle of incidence, i ( )

7.1 Reflection at a spherical surface

Spherical mirror is a reflecting surface
that is part of a sphere.

Concave Convex
(curves inward) (curves outward)

Terms used for spherical mirror

VV

1. Center of curvature, C 3. Pole or vertex, V
is defined as the center of the sphere is defined as point at the center of
of which a curved mirror forms a part. the mirror.

2. Radius of curvature, R 4. Principle axis, P
is defined as distance from the pole, is defined as straight line passing
V to the center of curvature, C. through V and C of a spherical mirror.

FOCAL POINT, AND FOCAL LENGTH,

After reflection from the mirror, parallel Parallel incident rays diverge

incident rays converge (come after reflection as if they had
originated from a focal point, F
together) at the focal point , F.
behind the mirror
Focal point, is defined as a point at
midway between center of curvature and Radius of curvature for a
pole. spherical mirror :

Focal length, is defined as the distance
between the pole and the principal focus
of a spherical mirror.

Ray diagram for obtaining images formed by

spherical mirrors

o The simple graphical method to indicate the positions and characteristics
of image formed by spherical mirror.

Concave Steps Locate O,F,C, mirror Convex

1 mirror 1 mirror
3
2 Draw OPF line 1 Use broken
2 lines for any
P Draw OFP line Draw rays or image
behind mirror
2any
3 C I P C
O two
F IF
2 O Draw OCO line
3
Real (in front mirror) Intersection point of Virtual (behind mirror)
the lines is the Upright
Inverted 1 position of image, Diminished
Diminished

Ray diagrams and characteristics of image
formed by concave mirrors

u>R u=R f<u<R

O

O CI V F V IC P
C OF
F

Front back I back
Front

Front back

 Real  Real  Real
 Inverted  Inverted  Inverted
 Diminished  Same size  Magnified

Ray diagrams and characteristics of image
formed by concave mirrors

u<f

Front F back I

C O P

 Virtual
 Upright
 Magnified

Ray diagrams and characteristics of image
formed by convex mirrors

Any position in P C
front of the
O IF
convex mirror
front back

 Virtual
 Upright
 Diminished

SPHERICAL MIRROR EQUATION MAGNIFICATION

Magnified
Diminished
ℎ Same size
ℎ
In problem solving, the appropriate
sign convention for the known
quantities must be put into equation
Quantity (+)ve (‒)ve

Real Virtual

(front side of mirror) (back side of mirror)

Real Virtual

(front side of mirror) (back side of mirror)

concave convex

Upright Inverted

(same orientation to the (opposite orientation to
object) the object)

Example 7.1 (b) the position of her image (d) the height of the image.
A woman who is 1.5 m

tall is located 3.0 m

from an convex anti
shoplifting mirror.

The focal length of
the mirror is 0.25 m.
m
Find :
(a) the radius of m (e) State the characteristics
(c) the magnification of the image formed.
curvature of the
mirror

o ‒(ve)  Virtual

m o +(ve)  Upright
o < 1  Diminished

TYPES OF IMAGE FORMED

Real Virtual

formed by actual light rays formed when the light rays
pass through the image do not pass through the
point.
image point but appear to
diverge from that point.

can be displayed on cannot be displayed on
screen. screen.

RECALL PRIOR KNOWLEDGE

Refraction is the bending of a light when it enters a medium
where its speed is different.

Index of refraction, is description of the
speed of light in a medium.

Greater the value of the refractive index of a med
ium, the greater is the “bending” effect of light wh
en it
passes from air into that medium.
Light travelling from:
o denser medium to less dense medium – Bend

away from normal
o less dense medium to denser medium – Bend

towards normal

7.2 Refraction at a spherical surface

A refracting surface is the part of a sphere
separating two transparent medium.

The spherical refracting surfaces are of two types :
o Convex spherical refracting surface
o Concave spherical refracting surface

Medium 1 Medium 2 Medium 1 Medium 2


Covex Concave
surface surface

EQUATION FOR SPHERICAL REFRACTING SURFACE

Light is originated For any spherical refracting surface,
from object, O

where

: object distance from pole

: image distance from pole

: Radius of curvature of the
spherical surface
Quantity (+)ve (‒)ve
: refractive index of medium 1

Real (front side) Virtual (back side) (medium containing incident ray)

Real Virtual : refractive index of medium 2

(opposite side of object) (same side as object ) (medium containing refracted ray)

convex concave

Example (a) Calculate the image distance
A coin is embedded in a Coin is the object. Ray travel from glass into air.
solid glass sphere of
radius 30 cm as shown u = + 20 cm
in figure below. The n1 = 1.5 (glass) , n2 = 1.0 (air)
refractive index of the r = ─ 30 cm (concave)
glass sphere is 1.5 and
the coin is 20 cm from
the surface.
m

(b) State the location of the image
Image formed same side as object.
Light is originated
from object, O

7.3 Thin lenses

A transparent material with two spherical refracting surfaces
whose thickness is thin compared to the radii of curvature of
the two refracting surfaces.

Convex Concave
(thick in the middle) (thin in the middle)

Terms used for Thin lenses



C2 O C1 C1 O C2


1. Principle axis, P
is defined as a line through the center of curvature C1 & C2 .

2. Center of the lens , O
is defined as a point where all rays pass through this point continue in a straight line.

3. Radius of curvature,
is defined as the radius of the sphere of which the surface of the lens is a part.

FOCAL POINT, AND FOCAL LENGTH,

Focal point, is defined as a point where Focal length, is defined as distance
the parallel rays incident on the lens either: between focal point, F & center of the
lens, O.
o converge after refraction for a convex

lens or

o diverge after refraction for a concave

lens.

Ray diagram for obtaining images formed by

concave and convex lenses

o The simple graphical method to indicate the positions and characteristics
of image formed by thin lenses.

Steps Locate O,F,C, lens Convex  Real
back  Inverted
Draw OPF line Draw O Front
Draw OFP line any  Magnified
Draw OCO line two F
I

F

Intersection point of
the lines is the
position of image,

Ray diagrams and characteristics of image
formed by convex lenses

u>2f O 2F1 F1 I  Real
u=2f Front  Inverted
F2 2F2  Diminished

back

O F1 F2 2F2  Real
back  Inverted
2F1 I  Same size

Front

f <u<2f 2F1 O F1 I  Real
Front  Inverted
F2 2F2  Magnified
back

u=f O F2 2F2  Real or virtual
back  Formed at infinity
2F1 F1

Front

u<f u at infinity
u at infinity,
 Virtual v=f
 Upright
 Magnified

I FO F

Front back

Any position in front of the concave lens

Ray diagrams and O FI F
characteristics of image Front back
formed by convex lenses

 Virtual
 Upright
 Diminished

THIN LENS EQUATION MAGNIFICATION

O I



Quantity (‒)ve Magnified

(+)ve Virtual Diminished

Real (back side of lens) Same size

(front side of lens) Virtual In problem solving, be careful to use the
appropriate signs for all the known
Real (front side of lens) quantities (as well as linear magnification
formula). The final answer will also have
(back side of lens) concave a sign, which gives additional information
about the image.
convex Inverted

Upright (opposite orientation to
the object)
(same orientation to the

object)

LENS MAKER’S EQUATION

o used to find the focal length of a lens.

where : focal length of the lens
: refractive index of the lens material
: refractive index of the medium

: radius of curvature for the 1st refracting surface
: radius of curvature for the 2nd refracting surface

Quantity (+) ve (‒) ve (∞)
convex concave Flat


Always seen from object position where light ray originated

R1 R2 R1 R2 R1 R2
(+ve) (─ve) (+ve) () (+ve) (+ve)

Biconvex Plano-convex Convex meniscus

R1 R2 R1 (R2) R1 R2
(ve) (+ve) (ve) (+ve) (+ve)

Biconcave Plano-concave Concave meniscus

Example (ii) If an object of height 0.5 cm is placed
A plano-convex lens has refractive index 10.0 cm in front of the lens, determine
1.66. The radius of curvature of the the size and characteristics of the image.
convex surface is 5.28 cm.
(a) Calculate the focal length of the
= +
lens.

= + cm

=



=


= = − . = − cm

cm o Real
Image is 2 cm height o Inverted
o enlarged

DO NOT CONFUSE BETWEEN

EQUATION FOR DETERMINE FOCAL LENGTH OF ....

MIRROR LENS




Lenses in combination Not in Curicculum specification
Serve as extra concept for you

The analysis of multi-lens systems (lenses in combination) requires only one new

rule : The image of the first lens acts as the object for the second lens

(this is where object distances may be negative)

① Ignoring lens 2, apply + = locate
③ Apply + = to get the final
image I1 produced by lens 1.
Lens 2
Lens 1
image, I2

Total magnification

is the product of

the magnification of
each lens



② I1 serves as object for Lens 2 (O2). Determine Magnification Magnification
the distance of I1 from lens 2 ( ) due to lens 1 due to lens 2


= − = −

NEXT TOPIC …

PHYSICAL OPTICS

TOPIC 8 Physical optics is the
PHYSICAL OPTICS study of light as a wave
phenomenon.
LECTURE F2F SLT : 2 HOURS Some phenomena such
TUTORIAL F2F SLT : 8 HOURS (INCLUDING PRE & POST LAB EXP 6) as interference &
diffraction can only be
explained by treating
light as wave.

Subtopics :
8.1 Huygen’s Principle
8.2 Constructive interference and destructive interference
8.3 Interference of transmitted light through

double slits
8.4 Interference of reflected light in thin film
8.5 Diffraction by a Single slit
8.6 Diffraction Grating

PREPARED BY CHONGYL & SULAIMAN PHYSICS UNIT KMJ SESSION 2020/2021