# Physics 9702 Doubts | Help Page 138

__Question 682: [Current of Electricity]__**(a)**

(i) On Fig.1, sketch I – V
characteristic for a filament lamp.

(ii) Explain how resistance of the
lamp may be calculated for any voltage from its I – V characteristic.

**(b)**Two identical filament lamps are connected first in series, and then in parallel, to a 12 V power supply that has negligible internal resistance. The circuits are shown in Fig.2 and Fig.3 respectively.

(i) State and explain why resistance
of each lamp when they are connected in series is different from the resistance
of each lamp when they are connected in parallel.

(ii) Each lamp is marked with a rating
‘12 V, 50 W’. Calculate total resistance of the circuit for the two lamps
connected such that each lamp uses this power.

**Reference:**

*Past Exam Paper – June 2011 Paper 23 Q5*

__Solution 682:__**(a)**

(i) The curve starts from (0,0) and is
a smooth curve in correct direction.

Curve
correct for end section never horizontal
(ii) Resistance R = V / I, hence we take
the co-ordinates of V and I at a point from graph and calculate the ratio V / I.

**(b)**

(i) Each lamp connected in parallel
has a greater p.d. / greater current across it {since
the overall resistance in the circuit is less, the current is higher}. So,
the lamp gets hotter. {The resistance of a lamp is not
constant. As the current passes through it, the lamp gets hotter and thus, its
resistance increases. This is indicated in the graph drawn in part (a). As the
resistance of each of the lamps become greater, the combined resistance of the
parallel combination increases.} Thus, the resistance of the lamps in
parallel become greater.

(ii)

Power P = V

^{2}/ R or Power P = VI and V = IR
Resistance R {= V

^{2}/ P = 12^{2}/ 50} = 144 / 50 = 2.88 Ω for each lamp
{For parallel combination,
total resistance = (1/2.88 + 1/2.88)

^{-1}= 1.44 Ω}
Total Resistance = 1.44 Ω

__Question 683: [Measurement + Resistance]__
Resistance R of a uniform metal wire
is measured for different lengths

*l*of the wire. Variation with*l*of R is shown in Fig.1.**(a)**Points shown in Fig.1 do not lie on the best-fit line. Suggest a reason for this.

**(b)**Determine gradient of the line shown in Fig.1.

**(c)**Cross-sectional area of the wire is 0.12 mm

^{2}.

Use answer in (b) to determine
resistivity of the metal of the wire.

**(d)**Resistance R of different wires is measured. Wires are of the same metal and same length but have different cross-sectional areas A.

On Fig.2, sketch a graph to show
variation with A of R.

**Reference:**

*Past Exam Paper – November 2014 Paper 21 Q3*

__Solution 683:__**(a)**The scatter of the points is due

__random error__(in the measurements) of the length OR resistance

{Systematic error is
associated with the apparatus and would produce a similar error for all the
measurements.}

**(b)**{Consider points (0.8, 3.6) and (0.4, 1.9)}

Gradient = (3.6 – 1.9) / (0.8 – 0.4)
= 4.25

**(c)**

Resistance R = ρl / A

{Resistivity ρ = RA /

*l*= (R/*l*) A}
Resistivity ρ = gradient × area =
4.25 × (0.12 × 10

^{–6}) = 5.1(0) × 10^{–7}Ω m**(d)**The graph should show the resistance decreasing with increasing area.

Correct shape with curve being
asymptote to both axes

{R = ρ

*l*/A. R is proportional to 1/A.}

__Question 684: [Kinematics]__
Variation with time t of velocity v
of a car is shown in Fig.1.

At time t = 0, driver sees an
obstacle in the road. A short time later, driver applies the brakes. The car
travels in two stages, as shown in Fig.1.

**(a)**Use Fig.1 to describe the velocity of the car in

1. stage 1,

2. stage 2.

**(b)**

(i) Calculate distance travelled by
the car from t = 0 to t = 3.5 s.

(ii) Car has a total mass of 1250
kg. Determine total resistive force acting on the car in stage 2.

**(c)**For safety reasons drivers are asked to travel at lower speeds. For each stage, describe and explain effect on the distance travelled for the same car and driver travelling at half the initial speed shown in Fig.1.

(i) stage 1:

(ii) stage 2:

**Reference:**

*Past Exam Paper – November 2011 Paper 23 Q2*

__Solution 684:__**(a)**

1. Constant velocity / speed

2.

EITHER constant / uniform decrease
(in velocity/speed)

**(b)**

(i)

The distance travelled is given by
the area under graph for both stages.

Stage 1: {area
of rectangle} distance (18 × 0.65) = 11.7 (m)

Stage 2: {area
of triangle} distance = (½ × 18 × [3.5 – 0.65]) = 25.7 (m)

Total distance {= 11.7 + 25.7} = 37.(4) m

(ii)

EITHER

F = ma

Acceleration a = (18 – 0) / (3.5 –
0.65)

Force F = 1250 × 6.3 =7900 N

OR

E

_{K}= ½ mv^{2 }= ½ × 1250 × (18)^{2}
{Force × distance = work done = E

_{K}. F × 25.7 = E_{K}}
F = ½ × 1250 × (18)

^{2}/ 25.7 = 7900 N
OR

Initial momentum = 1250 × 18

F = change in momentum / time taken =
(1250 × 18) / 2.85 = 7900

**(c)**

(i)

{Here, the speed is
constant, that is, the acceleration is zero. Speed = distance / time.

Distance = speed × time. If speed is halved, the distance travelled is also halved.}

EITHER half / less distance as speed
is half / less

OR half distance as the time is the
same

{By moving at a lower
speed, the reaction time of the driver may be faster. That is the time is
shorter.}

OR sensible discussion of reaction
time

(ii)

{v

^{2}= u^{2}+ 2as. Here the initial speed u is now halved. Final speed is zero. The acceleration / deceleration is constant. Here, the time to stop the car will also be less since the speed is lower.
When initial speed is u,
Distance s

_{1}= u^{2}/ 2a
When initial speed is u/2,
Distance s

_{2}= (u/2)^{2}/ 2a = u^{2}/ 8a = s_{1}/4}
EITHER same acceleration and s = v

^{2}/ 2a
OR v

^{2}(for this) has now become ¼ v^{2}
So, the distance travelled will be ¼
of the distance travelled {when the speed is not
halved}

__Question 685: [Current of Electricity]__
Fig.1 shows a 12 V power supply with
negligible internal resistance connected to uniform metal wire AB.

Wire has
length 1.00 m and resistance 10 Ω. Two resistors of resistance 4.0 Ω and 2.0 Ω
are connected in series across the wire.

Currents І

_{1}, І_{2}and І_{3}in the circuit are as shown in Fig.1.**(a)**

(i) Use Kirchhoff’s first law to
state relationship between І

_{1}, І_{2}and І_{3}.
(ii) Calculate I

_{1}.
(iii) Calculate the ratio x, where

x = power in metal wire / power in series resistors:

**(b)**Calculate potential difference (p.d.) between the points C and D, as shown in Fig.1. Distance AC is 40 cm and D is the point between the two series resistors.

**Reference:**

*Past Exam Paper – November 2012 Paper 22 Q5 & Specimen 2016 Paper 2 Q5*

__Solution 685:__**(a)**

(i) I

_{1}= I_{2}+ I_{3}
(ii)

I

_{1}is the total current in the circuit.
I = V / R or I

_{2}= 12/10 = 1.2A
R = [1/(2+4) + 1/10]

^{-1}= 3.75Ω or I_{3}= 12/6 = 2.0A
I

_{1}= 12/3.75 = 3.2A or I_{1}= 1.2 + 2.0 = 3.2A
(iii):

Power = VI OR I

^{2}R OR V^{2}/R
x = (I

_{2}^{2}R_{w}) / (I_{3}R_{s}) OR (VI_{2}) / (VI_{3}) OR (V^{2}/R_{w}) / (V^{2}/R_{s})
(choosing P=VI)

x = (12 ×
1.2) / (12 ×
2.0) = 0.60

**(b)**{p.d. V is proportional to resistance R [V = IR] and the resistance R of a wire is proportional to the length of the wire, L [R = ρL/A].

So, V is proportional to
L. The wire is in parallel with the power supply, so the p.d. across AB (total
length of the wire) is the same (= 12V) as the e.m.f. from the power supply. When
the total length L of the wire is taken in account [point C is at point B], the
p.d. across AC is 12V. As the length AC is decreased, the p.d. across AC will
also decrease.

Now, point A and B are
fixed and are connected to the terminals of the supply. The positive terminal
of the supply and point A are at a potential of 12V. The negative terminal of
the supply and point B are at a potential of 0V.

But, the p.d. V across AC
is a potential difference – that is, a difference in potential.

When point C is 40cm from
point A, p.d. across AC is 12 × (0.4/1)
= 4.8V. This is a (p.d.) difference in potential. Since point A is at a
potential of 12V, and the difference in potential between AC is 4.8V, point C
will be at a potential of 12 – 4.8 = 7.2V. Point B is at 7.2V and point C is at
0V, so the p.d. across BC = 7.2V}

Since wire is 1m, p.d. across AC =
12 ×
(0.4/1)V and across BC = 12 – (12 × 0.4/1)V.

p.d. BC = 12 – (12 × 0.4)
= 7.2V or p.d. AC = 4.8V

{Similarly, the total p.d.
across resistors in series is the sum of p.d. across each resistor. So, across
BD, p.d. = (12 × 2/6) or (12 – (12 × 4/6)) = 4.0V and p.d.
across AD = (12 × 4/6) = 8.0V. This is the potential divider equation.
Point D is at a potential of 4.0V}

p.d. BD = 12 – (12 ×
4/6) = 4.0V or p.d. AD = 8.0V

p.d. between points C and D is the difference
in potential.

p.d. = 7.2 – 4.0 = 3.2V or p.d. = 8.0 – 4.8 =
3.2V

{

**Question:**
Why the pd between C and D
has to be: pd of AD - pd of AC or pd of BC - pd of BD I just don't understand
why. The current is in the same directions especially in BC and BD. Why are we
subtracting them?

**Explanation:**

To find the p.d. between C
and D, we need to find the potential at C and that at D and then take the difference.

Facts:

(1) Current flows from the
+ve terminal of the supply.

(2) The –ve terminal of
the supply is taken to be 0V and the +ve terminal is taken to be +12V. Any
point connected directly to the +ve terminal (example: point A) is also at 12V
and any point connected directly to the –ve terminal (example: point B) is at
0V. So, as we move from A to B, the potential decreases.

Potential DIFFERENCE (p.d.)
between A and C = Potential at A – Potential at C

p.d. between A and C can
be obtained from Ohm’s law: V = I

_{2}R. The resistance of a wire is proportional to its length (R = ρL / A). 100cm corresponds to a resistance of 10Ω. 40cm corresponds to a resistance of (0.4 / 1) × 10 = 4Ω.
p.d. between A and C = I

_{2}R = 1.2 × 4 = 4.8V
Potential at C = Potential
at A – p.d.between A and C = 12 – 4.8 = 7.2V

p.d. between A and D =
Potential at A – Potential at D

p.d. between A and D =
p.d. across the 4.0Ω
resistor = I

_{3}(4.0) = 2.0 × 4.0 = 8.0V
Potential at D = 12 – 8.0
= 4.0V

Potential difference
between C and D = 7.2 – 4.0 = 3.2V}

__Question 686: [Vectors]__
Vector quantity V is resolved into
two perpendicular components X and Y. Angle between V and component X is θ.

Angle between component X and the
vector V is increased from 0° to 90°.

How do magnitudes of X and Y change
as the angle θ is increased in this way?

X Y

A increase
increase

B increase
decrease

C decrease
increase

D decrease
decrease

**Reference:**

*Past Exam Paper – June 2010 Paper 11 Q5 & Paper 12 Q6 & Paper 13 Q2*

__Solution 686:__**Answer: C.**

When the angle θ is zero, the vector X would be the exactly same
as vector V. In this situation, vector V does not have any component along Y.
So here, vector Y would be zero. Vector X would have the maximum value here.

As the angle θ is increased, the
magnitude of vector V is shared between a component along X and another
component along Y. So, as the angle θ increases, the magnitude of X decreases
while that of Y increases.

When the angle is 90°, the vector Y
would be exactly the same as vector V. In this situation, vector V does not
have any component along X. So, here, vector Y would be zero.

21/O/N/14 Q.4

ReplyDelete22/O/N/14 Q.1

For 21/O/N/14 Q.4, check solution 692 at

Deletehttp://physics-ref.blogspot.com/2015/05/physics-9702-doubts-help-page-140.html

For 22/O/N/14 Q.1, check solution 688 at

http://physics-ref.blogspot.com/2015/05/physics-9702-doubts-help-page-139.html

Can you explain June 2006 paper 4 Q 2 b (ii)?

ReplyDeleteCheck question 690 at

Deletehttp://physics-ref.blogspot.com/2015/05/physics-9702-doubts-help-page-139.html

In Q 682 , why was the parallel circuit chosen? Based on the wordings of the question "the two lamps connected such that each lamp uses this power", I thought each lamp must use 50W, and that this is only possible in the series circuit since current is constant in series (because P = IV). But in parallel, the current is distributed across the wires, so current is less in each lamp, so doesn't each lamp use less power?

ReplyDeleteIf the overall resistance in the circuit is R, the total current in the circuit is I = V / R. In parallel, the overall resistance is less and so, I is greater. In series, the overall resistance R is greater, and so, I is smaller.

Delete+ In parallel, the p.d. across each lamp is equal to the e.m.f. of the supply. In series, the p.d. is divided between the lamps such that the total is equal to the e.m.f.

Thank you so much for all your help and this whole website! God bless you!

DeleteIn Solution 685, I don't understand why the pd between C and D has to be:

ReplyDeletepd of AD - pd of AC

or

pd of BC - pd of BD

I just don't understand why. The current is in the same directions especially in BC and BD. Why are we subtracting them?

Explanations have been added at the end of the question.

Deletecan you please give explanation of 9702 may june 2005 q2

ReplyDeletepaper 2

DeleteSee solution 1085 at

Deletehttp://physics-ref.blogspot.com/2015/12/physics-9702-doubts-help-page-230.html

can you please explain 9702 may june 2005 q4 (c)

ReplyDeletewhich paper?

Deletepaper 2

DeleteI know that solution 288 is there for than question but I still don't understand so it will be better if u explain in more detail. thanks

DeleteLet me know exactly what you are not understanding at the post with solution 288. It would be easier to explain then.

Deletecan u please explain

Deletefor the hard ball I dont understand how is all kinetic energy converted to strain energy

ReplyDeleteStrain energy is the energy stored in an object undergoing deformation – here compression.

Deletenow, go through the explanations at

http://physics-ref.blogspot.com/2015/01/physics-9702-doubts-help-page-48.html

again

but it is mentioned that hard ball doesn't undergo deformation

Deleteplease reply

DeleteUpon collision, the hard ball is momentarily at rest (EK = 0). But from the law of conservation of energy, its previous KE cannot be destroyed, it should have been converted into another form of energy. The hard ball does not deform, so the KE does not become strain energy of the hard ball. In fact, its KE has been converted into strain energy of the glass. Since strain energy is associated with deformation, as all of the KE of the hard ball have completed been converted into strain energy of the glass, the glass is more likely to deform, that is, break.

DeleteAs for the soft ball, as it collides with the glass it compresses. Thus some of the KE of the soft ball is converted into strain energy of the soft ball. The remaining amount of energy is converted into strain energy of the glass. Hence, comparing the hard and soft balls, more energy has been converted into strain energy of the glass for the collision of the hard ball. So, the glass is more likely to break with the hard ball.

thanks

DeleteCould you solve (Oct/Nov 2015 Variant 22 Q6) please? I dont know why I feel like all the concepts are so different..

ReplyDeleteSee solution 1106 at

Deletehttp://physics-ref.blogspot.com/2016/04/physics-9702-doubts-help-page-237.html

I'm sorry, but I don't understant 684 bii about the resistive force at all. Could you elaborate?

ReplyDeleteResultant force F = ma. Deceleration or Acceleration = gradient of stage 2 on graph. Consider points (3.5, 0) and (0.65, 18). Acceleration = (18 – 0) / (0.65 – 3.5) = - 6.3 ms-2. Deceleration = 6.3 ms-2.

DeleteAlso, constant speed is it constant magnitude as in 40m/s horizontal line in a graph or constant as in constant increase that happens when acceleration is >0 but constant? Then what about accelerating? Does it mean accelerate uniformly or what?

ReplyDeleteStage 1 is constant velocity of 18m/s. That is, it continues to travel at this speed.

DeleteStage 2 is constant deceleration. that is, the speed is decrease by equal amount in equal interval of time.

In solution 684,F is the resultant force but we have to calculate frictional force ! So why we haven't calculated mg-friction force=ma

ReplyDeletethe motion is usually considered to be horizontal. the weight, which is vertically down, does not affect the motion

Delete