# Case Study Questions Science Class 10th

## Case Study Question 01

Question.1.
When three resistors are connected in series with a battery of voltage V and voltage drop across resistors is V_{1}, V_{2} and V_{3}, which of the relation is correct?

(a) V = V_{1} = V_{2} = V_{3}
(b) V = V_{1}+V_{2}+V_{3}
(c) V_{1}+V_{2}+V_{3} = 3V
(d) V > V_{1}+V_{2}+V_{3}

(b) : In series combination, the total voltage is equal to the sum of voltage drop across each resistance.

Question.2.
When the three resistors each of resistance R Ω, connected in series, the equivalent resistance is

(a) \frac{R}{2}
(b) > R
(c) < \frac{R}{2}
(d) < R

(b) : R_{S}=R_{1}+R_{2}+R_{3}
So, R_{S}= R + R + R = 3R

Question.3.
There is a wire of length 20 cm and having resistance 20 Ω cut into 4 equal pieces and then joined in series. The equivalent resistance is

(a) 20 Ω
(b) 4 Ω
(c) 5 Ω
(d) 10 Ω

(a) : Resistance of each wire = \frac{20}{4} = 5 Ω
Equivalent resistance in series
R_{S}= 5 + 5 + 5 + 5
⇒ R_{S}= 20 Ω

Question.4.
In the following circuit, find the equivalent resistance between A and B is (R = 2 Ω)

(a) 10 Ω
(b) 5 Ω
(c) 2 Ω
(d) 4 Ω

(a) : All are in series, R_{S} = 5R = 5 × 2 = 10 Ω

Question.5.
In the given circuit, the current in each resistor is

(a) 3 A
(b) 6 A
(c) 9 A
(d) 18 A

(a) : R_{S} = 1 + 2 + 3 = 6 Ω
I=\frac{18}{6}=3A

## Case Study Question 02

Question.1.
What are the properties of heating element?

(a) High resistance, high melting point
(b) Low resistance, high melting point
(c) High resistance, low melting point
(d) Low resistance, low melting point.

(a) : Heating element must have high resistance and high melting point.

Question.2.
What are the properties of electric fuse?

(a) Low resistance, low melting point
(b) High resistance, high melting point.
(c) High resistance, low melting point
(d) Low resistance, high melting point

(c) : Electric fuse must have high resistance and low melting point.

Question.3.
When the current is doubled in a heating device and time is halved, the heat energy produced is

(a) doubled
(b) halved
(c) four times
(d) one fourth times

(a) : Given: H=I^{2}Rt
So, H′ = (2I)^{2}\frac{R}{2}t = 2H

Question.4.
A fuse wire melts at 5 A. It is is desired that the fuse wire of same material melt at 10 A. The new radius of the wire is

(a) 4 times
(b) 2 times
(c) \frac{1}{2} times
(d) \frac{1}{4} times

(b) : Given: I = 5 A, resistance = R. Let r be the new radius.
Now, H = I^{2}Rt …(i)
Also H′ = H’=(I’)^{2}R’t …(ii)
From (i) and (ii),
5^{2}\times \rho \frac{L}{\pi r^{2}}t=10^{2}\times \rho \frac{L}{\pi r’^{2}}t
⇒ \frac{25}{r^{2}}=\frac{100}{r’^{2}}
⇒ \frac{r’}{r}=2
⇒ r′ = 2r

Question.5.
When a current of 0.5 A passes through a conductor for 5 min and the resistance of conductor is 10 Ω, the amount of heat produced is

(a) 250 J
(b) 5000 J
(c) 750 J
(d) 1000 J

(c) : Given: I = 0.5 A, R = 10 Ω, t = 5 min
H = I^{2}Rt = 0.5 × 0.5 × 10 × 5 × 60
H = 750 J

## Case Study Question 03

Ohm’s law is the relationship between potential difference and current in a circuit which was first established by George Simon Ohm. The law states that the current passing through a metallic conductor is directly proportional to the potential difference applied between its ends. V ∝ I i.e., V = kI where k is the resistance offered by the conductor and is constant for a given conductor. Although a large class of materials is known to follow Ohm’s law, there do exist materials used in circuits that do not follow the direct relationship between V & I.

Question.1.
If in a circuit both the potential difference and resistance are doubled, then

(a) current is doubled.
(b) current is halved.
(c) current remains same.
(d) current is four times.

(c) Current remains same

Question.2.
When a battery of 9 V is connected across a conductor and the current flowing is 0.1 A, the resistance is:

(a) 90 Ω
(b) 0.9 Ω
(c) 9 Ω
(d) 900 Ω

(a) 90 Ω

Question.3.
By increasing voltage across a conductor:

(a) current will increase.
(b) current will decrease.
(c) resistance will decrease.
(d) resistance will increase.

(d) resistance will increase

Question.4.
The slope of the V-I graph shall give:

(a) resistance
(b) reciprocal of resistance
(c) power
(d) charge

(a) resistance

Question.5.
Four students have plotted the graph between V-I for a conductor. Which one is correct?

(a)(b)(c)(d)

(c)

## Case Study Question 04

Refer the figure below carefully and answer the following questions:

In a circuit, several resistors may be combined to form a network. The combination must have two endpoints to connect it with a battery or other elements of the circuit. When the resistors are connected in series then the current flowing in each remains the same but potential differences across each resistor will vary. When the resistances are connected in parallel, the potential difference across each resistor will be the same though a different amount of current will flow in each resistor.

Question.1.
The household circuits are connected in:

(a) series
(b) parallel
(c) both series and parallel
(d) neither series nor parallel

(b) parallel

Question.2.
The equivalent resistance of two resistors x and y is Z when connected in series and M when connected in parallel. Z:M is:

(a) xy
(b) x+y\times y
(c) \frac{(x+y)^{2}}{xy}
(d) xy(2x+2y)

(c) \frac{(x+y)^{2}}{xy}

Question.3.
Two resistances 10 Ω and 3 Ω are connected in parallel across a battery. If there is a current of 0.2 A in 10 resistors, the voltage supplied by the battery is:

(a) 2 V
(b) 1 V
(c) 4 V
(d) 8 V

(a) 2 V

Question.4.
Two wires each having a resistance value equal to R are first connected in series and then connected in parallel. The plot shows the graphical representation of resistances in both cases.

(a) A denotes parallel combination
(b) B denotes series combination
(c) A denotes series combination and B denotes parallel combination
(d) None of the above

(c) A denotes series combination and B denotes parallel combination

Question.5.
The equivalent resistance (in Ω) of the network across A and B is:

(a) 2 Ω
(b) 1.5 Ω
(c) 2.5 Ω
(d) 3 Ω

(a) 2 Ω

## Case Study Question 05

Refer the figure below carefully and answer the following questions:

Resistivity or electric resistivity is the inverse of the electrical conductivity. Resistivity is a fundamental property of a material and it demonstrates how strongly the material resists or conductselectric current. A low resistivity is a clear indication of a material which readily allows electric current. The common representation of resistivity is by the Greek letter ρ. Also, the SI unit of electrical resistivity is ohm-meter (Ω-m). Resistivity refers to the electrical resistance of a conductor of a particular unit cross-sectional area and unit length. Experts can use resistivity for comparing different materials on the basis of their ability to conduct electric currents. High resistivity is the designation of poor conductors.

Question.1.
The value of resistivity depends upon:

(a) length of wire
(b) area of cross section
(c) nature of conductor

(c) nature of conductor

Question.2.
A wire has the same resistance as the one given in the figure. Calculate its resistivity if the length of the wire is 10 m and its area of cross section is 2 m.

(a) 16 Ω – m
(b) 8 Ω – m
(c) 16 kΩ – m
(d) 8 kΩ – m

(b) 8 Ω – m

Question.3.
The resistivity of alloys is:

(a) very low
(b) very high
(c) generally lower than its constituent metals
(d) more than resistivity of insulators

(a) very low

Question.4.
A student plotted the graphs as shown below to study the variation of resistances R of a wire with its length l and radius r:

(I) The resistance of a wire is inversely related to the length ofthe wire, i.e., R\ \alpha \ \frac{1}{l} .
(II) The resistance of a wire is directly related to the length of the wire, i.e., R\ \alpha \ l.
(III) The resistance of a wire is inversely related to the radius of the wire, i.e., R\ \alpha \ \frac{1}{r}.
(IV) The resistance of a wire is inversely related to the square of the radius of the wire, i.e., R\ \alpha \ \frac{1}{r^{2}}.

(a) Both (I) and (III)
(b) Both (II) and (III)
(c) Both (I) and (IV)
(d) Both (II) and (IV)

(d) Both (II) and (IV)

Question.5.
A wire of length l and of radius of cross-section r has a resistance of R Ω. Another wire of same material and of radius of cross section 2r will have the same R if the length is:

(a) \frac{l}{4}
(b) 2l
(c) 4l
(d) \frac{l}{2}

(c) 4l

## Case Study Question 06

The electrical energy consumed by an electrical appliance is given by the product of its power rating and the duration for which it is used. SI unit of electrical energy is the joule. Where a large quantity of energy is involved, using a joule is not convenient as a unit. So, for commercial purposes, bigger units of electrical energy are involved. 1 kilowatt-hour is equal to 3.6\times 10^{6}  joules of electrical energy.

Question.1.
The value of energy dissipated by a certain heater is E. If the duration of operation of the heater is doubled, the energy dissipated will be:

(a) halved
(b) doubled
(c) four-times
(d) remains same

(b) doubled

Question.2.
60 W is the power of a lamp. The energy dissipated in one minute is:

(a) 360 J
(b) 36 J
(c) 3.6 J
(d) 3600 J

(d) 3600 J

Question.3.
Calculate the energy transformed by a 5 A current flowing through a resistor of 2 Ω for 30 minutes.

(a) 90 kJ
(b) 80 kJ
(c) 60 kJ
(d) 40 kJ

(a) 90 kJ

Question.4.
Choose the correct statement:

(a) 1 watt-hour = 3600 J
(b) 1 kWh = 36\times 10^{6}  J
(c) Energy in kWh = power in W (watt) × time in hour (h)
(d) Energy in kWh = V × I × T1000

(a) 1 watt-hour = 3600 J

Question.5.
Choose the incorrect statement.

(a) Higher the resistance, the lesser the power consumed.
(b) Lower the resistance, more the voltage drawn.
(c) Higher the resistance, the higher the current flown.
(d) Higher the resistance, the lesser the voltage drawn.

(c) Higher the resistance, the higher the current flown.

## Case Study Question 07

The following graphs represent the current versus voltage and voltage versus current for six conductors A, B, C, D, E, and F.

Question.1.
Among conductors A, B, C, D, E, F, the maximum resistance is shown by:

(a) curve C
(b) curve A
(c) curve F
(d) curve D

(a) curve C

Question.2.
Which of the following does not indicate the resistance of curve B?

(a) The slope of curve B
(b) The ratio of V-intercept to I-intercept
(c) The ratio of total grids on the y-axis to total grids on the x-axis
(d) \frac{3}{4} Ω

(d) \frac{3}{4} Ω

Question.3.
Which indicates the correct sum of least resistances of two graphs?

(a) Curve C + Curve F
(b) Curve A + Curve D
(c) Curve A + Curve F
(d) Curve C + Curve D

(c) Curve A + Curve F

Question.4.
If resistances shown by curve A and curve E are added, the value will be:

(a) 1.83 Ω
(b) 1.50 Ω
(c) 1.64 Ω
(d) 1.25 Ω

(d) 1.25 Ω

Question.5.
Which is true for these graphs?

(a) Both are ohmic conductors
(b) Curve A is ohmic and B is non-ohmic conductor
(c) Both are non-ohmic conductors
(d) Curve B is ohmic and A is non-ohmic conductor

(c) Both are non-ohmic conductors

## Case Study Question 08

The graph below is a V-I graph of a metallic circuit drawn at two different temperatures T_{1} and T_{2}.

Question.1.
For the above graph choose the correct option depicting which of the two temperatures is higher with justification.

(a) T_{2} > T_{1}; Slope of V-I graph at T_{2} is greater than slope at T_{1}.
(b) T_{1} > T_{2}; resistance increases with increase in temperature.
(c) T_{2} > T_{1}; resistance increases with decrease in temperature.
(d) T_{1} > T_{2}; Slope of V-I graph at T_{1} is greater than slope at T_{2}.

(a) T_{2} > T_{1}; Slope of V-I graph at T_{2} is greater than slope at T_{1}.

Question.2.
For the above graph, at which temperature the resistance is higher?

(a) At T_{1}
(b) At T_{2}
(c) Resistance does not depend upon temperature
(d) None of these

(b) At T_{2}

Question.3.
Choose the correct set containing factors on which resistance depends?

(a) Length, Area of cross section, Temperature, Nature of the material.
(b) Area of cross section, Temperature, Nature of the material, Colour.
(c) Length, Area of cross section, Temperature, intermolecular attraction.
(d) Temperature, Nature of the material, Length, physical state of material.

(a) Length, Area of cross section, Temperature, Nature of the material.

Question.4.
What is likely to happen if current in a wire is passed for a longer time than required?

(a) The wire may get burnt and may melt.
(b) Length of the wire may decrease resulting in lower resistance.
(c) Resistance of wire will drop as it will be very difficult to stop the electrons.
(d) Resistance of the wire will get increased due to joule’s heating effect.

(d) Resistance of the wire will get increased due to joule’s heating effect.

Question.5.
If the vertical and horizontal axes of a typical V-I straight line graph are reversed, which graph below is likely to represent the IV graph? (I on vertical, V on horizontal for I-V graph).

(a) (A)
(b) (B)
(c) (C)
(d) (D)

(d) D

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