CBSE Class 10 Physics HOTs Electricity Set 03

Question. Name the electrical devices that are connected in the following part of the circuit.
Answer: 1-Ammeter, 2-voltmeter and 3-resistor

Question. What is an electric circuit? Distinguish between an open and a closed circuit.
Answer: An arrangement for maintaining the continuous flow of electric current by the electrical energy source through the various electrical components connected with each other by conducting wires is termed as electric circuit. An open circuit does not carry any current, while a closed circuit carries current.

TOPIC : Ohm’s Law and Factors on which the Resistance of a Conductor Depends

Question. Choose the incorrect statement regarding Ohm’s law.
(a) It is temperature independent
(b) It is valid for constant temperature
(c) It is valid for ohmic resistance
(d) It defines the relationship between potential difference and current through the conductor.
Answer: (a) It is temperature independent

Question. In Ohm‘s law, if physical condition of the conductor remains same, then
(a) \( I \propto V \)
(b) \( I \propto \frac{1}{V} \)
(c) \( I \propto V^2 \)
(d) \( I \propto \frac{1}{V^2} \)
Answer: (a) \( I \propto V \)

Question. For verifying Ohm’s law, we design an electric circuit diagram in which we show the arrangement of different circuit components. We find that with respect to resistor
(a) ammeter is connected in parallel and voltmeter in series.
(b) ammeter is connected in series and voltmeter in parallel.
(c) ammeter and voltmeter are both connected in series.
(d) ammeter and voltmeter are both connected in parallel.
Answer: (b) ammeter is connected in series and voltmeter in parallel.

Question. When a 4 V battery is connected across an unknown resistor there is a current of 100 mA in the circuit. The value of the resistance of the resistor is
(a) \( 4 \Omega \)
(b) \( 40 \Omega \)
(c) \( 400 \Omega \)
(d) \( 0.4 \Omega \)
Answer: (b) Given: V = 4 V, I = 100 mA = 0.1 A Using, V = IR
\( \implies \) \( R = \frac{V}{I} = \frac{4}{0.1} = 40 \Omega \)

Question. A cylindrical conductor of length ‘l’ and uniform area of cross-section ‘A’ has resistance ‘R’. Another conductor of length 2.5l and resistance 0.5R of the same material has area of cross-section
(a) 5 A
(b) 2.5 A
(c) 0.5 A
(d) \( \frac{1}{5} A \)
Answer: (a) Case I: \( R = \rho \frac{l}{A} \)
Case II: \( 0.5R = \rho \frac{2.5l}{A'} \)
On dividing, we get,
\( \implies \) \( A' = 5A \)

Electricity

Question. Resistance is directly proportional to temperature of the conductor.
(a) 9. (c)
(b) 10. (b) diameter (d) of the wire
(c) 11. (c)
(d) 12. (a)
Answer: (a) Resistance is directly proportional to temperature of the conductor.

Question. How much current will an electric bulb draw from 220 V source, if the resistance of the bulb is 1200 \( \Omega \)? If in place of bulb, a heater of resistance 100 \( \Omega \) is connected to the sources, calculate the current drawn by it.
Answer: Given : V : 220 V, \( R_1 = 1200 \text{ } \Omega \), \( I_1 = ? \)
\( R_2 = 100 \text{ } \Omega \), \( I_2 = ? \)
Using Ohm’s law, \( V = I_1R_1 \)
\( \implies \) \( I_1 = \frac{V}{R_1} = \frac{220}{1200} = 0.18 \text{ A} \)
and, \( I_2 = \frac{V}{R_2} = \frac{220}{100} = 2.2 \text{ A} \)

Question. 100 J of work is done in transferring 20 C of charge between two points in a conductor. Find the resistance offered by the conductor, if a current of 2A flows through it.
Answer: Given : \( W = 100 \text{ J} \), \( q = 20 \text{ C} \), \( I = 2 \text{ A} \), \( R = ? \)
Work done in carrying 20 C charge \( W = qV \)
From Ohm’s law, \( V = IR \)
\( \therefore W = q(IR) \)
\( \implies \) \( R = \frac{W}{qI} = \frac{100}{20 \times 2} = \frac{100}{40} = 2.5 \text{ } \Omega \)

Question. Priya has a copper wire and an aluminium wire of the same length. Can the electrical resistance of the two wires be the same? Justify your answer.
Answer: Yes, the electrical resistance of the two wires can be the same.
The reasons can be:
– The area of cross-section of the two wires is different.
– The thickness of the two wires is different.

Question. A piece of wire of resistance 20 \( \Omega \) is drawn out so that its length is increased to twice its original length. Calculate the resistance of the wire in the new situation.
Answer: Using, \( R = \rho \frac{l}{A} \),
We have, \( \frac{R_1}{R_2} = \frac{l_1}{l_2} \cdot \frac{A_2}{A_1} \)
Given : \( l_2 = 2l_1 \)
Volume of material will be conserved. So, \( A_1l_1 = A_2l_2 \)
\( \therefore \frac{A_1}{A_2} = \frac{l_2}{l_1} = 2 \);
\( \frac{R_1}{R_2} = \frac{l_1}{l_2} \cdot \frac{A_2}{A_1} = \frac{l_1}{2l_1} \cdot \frac{1}{2} = \frac{1}{4} \)
\( \therefore R_2 = 4R_1 = 80 \text{ } \Omega \)

Question. Two wires of equal lengths, one of copper and the other of manganin (an alloy) have the same thickness. Which one can be used for (i) electrical transmission lines, and (ii) electrical heating devices? Why?
Answer: (i) Copper, as it has the lesser resistivity.
(ii) Manganin, as it has the comparatively higher resistivity, less oxidation even at high temperature.

Question. The resistance of a metal wire of length 1 m is \( 10^4 \text{ } \Omega \) at 20 °C. If the diameter of the wire is 0.15 mm, find the resistivity of the metal at that temperature.
Answer: Radius of wire = \( 0.15/2 = 0.075 \text{ mm} = 0.075 \times 10^{-3} \text{ m} \)
Area of cross-section of wire = \( A = \pi r^2 \)
\( = 3.14 \times (0.075 \times 10^{-3})^2 \)
\( = 3.14 \times 0.005625 \times 10^{-6} \text{ m}^2 \)
\( = 1.76 \times 10^{-8} \text{ m}^2 \)
Using, \( \rho = R \frac{A}{l} \)
\( = \frac{10^4 \times 1.76 \times 10^{-8}}{1} \)
\( = 1.76 \times 10^{-4} \text{ } \Omega \text{m} \)

Question. (a) In a given ammeter, a student saw that needle indicates 12th division in ammeter while performing an experiment to verify Ohm’s law. If ammeter has 10 divisions between 0 to 0.5 A, then what is the ammeter reading corresponding to 12th division?
(b) How do you connect an ammeter and a voltmeter in an electric circuit?
Answer: (a) Least count of ammeter = \( \frac{0.5}{10} = 0.05 \text{ A} \)
Thus, the value corresponding to 12 divisions = \( 0.05 \times 12 = 0.6 \text{ A} \)
(b) The ammeter is connected in series and a voltmeter is connected in parallel in an electric circuit.

Question. (a) Write the relationship between electrical resistance and electrical resistivity for a metallic conductor of cylindrical shape. Hence derive the SI unit of electrical resistivity.
(b) Find the resistivity of the material of a metallic conductor of length 2 m and area of cross section \( 1.4 \times 10^{-6} \text{ m}^2 \). The resistance of the conductor is 0.04 ohm.
Answer: (a) \( \rho = R \frac{A}{l} \)
SI unit of \( \rho = \text{ohm} \times \frac{\text{m}^2}{\text{m}} = \text{ohm} \times \text{metre} \) or \( \Omega \text{m} \)
(b) \( \rho = R \frac{A}{l} \)
\( = \frac{0.04 \text{ } \Omega \times 1.4 \times 10^{-6} \text{ m}^2}{2 \text{ m}} \)
\( = 2.8 \times 10^{-8} \text{ } \Omega \text{m} \)

Question. (a) List the factors on which the resistance of a conductor in the shape of a wire depends.
(b) Why are metals good conductors of electricity whereas glass is a bad conductor of electricity? Give reason.
(c) Why are alloys commonly used in electrical heating devices? Give reason.
Answer: (a) The factors on which the resistance of a conductor in the shape of wire depends:
(i) Length of the conductor: Resistance is directly proportional to length of the conductor.
(ii) Area of cross section of the wire: The resistance is inversely proportional to area of cross section of the wire.
(iii) The resistance of the conductor depends on the nature of its material.
(iv) Temperature of the conductor: Resistance is directly proportional to the temperature of the conductor.
(b) Metals are good conductor of electricity as they have free electrons to conduct whereas glass is a bad conductor of electricity as it does not allow electric current to pass through it due to non-availability of free electrons.
(c) The alloys are commonly used in electric heating device. This is because:
(i) Alloy are combination of two or more metals.
(ii) Its resistivity is higher than that of its constituent metals.
(iii) It neither gets oxidised nor burn easily at high temperature.
(iv) It shows less rapid variations of resistivity due to change in temperature.

Question. (a) List the factors on which the resistance of a uniform cylindrical conductor of a given material depends.
(b) The resistance of wire of 0.01 cm radius is 10 \( \Omega \). If the resistivity of the wire is \( 50 \times 10^{-8} \text{ } \Omega\text{m} \), find the length of this wire.
Answer: (a) Resistance of a conductor depends upon:
(i) length of the conductor (l) [\( R \propto l \)]
(ii) Area of cross-section of the conductor (A) [\( R \propto \frac{1}{A} \)]
(b) Radius of wire, \( r = 0.01 \text{ cm} = 0.01 \times 10^{-2} \text{ m} = 10^{-4} \text{ m} \)
Resistance, \( R = 10 \text{ } \Omega \)
Resistivity, \( \rho = 50 \times 10^{-8} \text{ } \Omega\text{m} \)
Using, \( R = \rho \frac{l}{A} = \rho \frac{l}{\pi r^2} \)
\( \implies \) \( l = \frac{R \pi r^2}{\rho} \)

\( \implies \) \( l = \frac{10 \times 3.14 \times (10^{-4})^2}{50 \times 10^{-8}} = 0.628 \text{ m} \)

\( \implies \) \( l = 0.62 \text{ m} \)

TOPIC : Resistance of a System of Resistors

Question. If a person has five resistors each of value \( \frac{1}{5} \text{ } \Omega \), then the maximum resistance he can obtain by connecting them is
(a) \( 1 \text{ } \Omega \)
(b) \( 5 \text{ } \Omega \)
(c) \( 10 \text{ } \Omega \)
(d) \( 25 \text{ } \Omega \)
Answer: (a) For maximum resistance, all resistors should be connected in series.
\( \therefore R_s = R_1 + R_2 + R_3 + R_4 + R_5 \)
\( = \frac{1}{5} + \frac{1}{5} + \frac{1}{5} + \frac{1}{5} + \frac{1}{5} \)
\( = \frac{5}{5} = 1 \text{ } \Omega \)

Question. Two wires of same length and area made of two materials of resistivity \( \rho_1 \) and \( \rho_2 \) are connected in series to a source of potential V. The equivalent resistivity for the combination is
(a) \( \rho_1 + \rho_2 \)
(b) \( \frac{\rho_1\rho_2}{\rho_1 + \rho_2} \)
(c) \( \frac{\rho_1\rho_2}{\rho_1 + \rho_2} \)
(d) \( \left( \frac{\rho_1 + \rho_2}{2} \right) \)
Answer: (d) \( R = \rho \cdot \frac{2l}{A} = R_1 + R_2 \)
\( \rho \cdot \frac{2l}{A} = \rho_1 \frac{l}{A} + \rho_2 \frac{l}{A} = (\rho_1 + \rho_2) \frac{l}{A} \)
\( \rho = \frac{\rho_1 + \rho_2}{2} \)

Question. Two bulbs of 100 W and 40 W are connected in series. The current through the 100 W bulb is 1 A. The current through the 40 W bulb will be:
(a) 0.4 A
(b) 0.6 A
(c) 0.8 A
(d) 1 A
Answer: (d) 1 A

Question. In series combination of resistors, the flow of current across each resistor is
(a) initially increases then decreases
(b) increases continuously
(c) decreases continuously
(d) remains the same
Answer: (d) remains the same

Question. In your daily life experience, which of the following is not used in series combination?
(a) Decorative bulbs
(b) Fuses
(c) Domestic appliances
(d) All of the options
Answer: (c) Domestic appliances

Question. Pick out the incorrect statement from the following about series combination of resistors.
(a) The current across each resistor is the same.
(b) The potential difference is same across each resistor
(c) Equivalent resistance is larger than the largest resistor
(d) It is used to decrease the current in the circuit.
Answer: (b) The potential difference is same across each resistor

Question. Three resistors of resistance \( 1 \text{ } \Omega \), \( 2 \text{ } \Omega \) and \( 3 \text{ } \Omega \) are connected in series combination and draw the current 0.5 A from the power source. The potential difference across the combination is
(a) 3 V
(b) 12 V
(c) \( \frac{1}{12} \text{ V} \)
(d) 6 V
Answer: (a) 3 V

Question. The resistor \( R_1 \) and \( R_2 \) are connected in parallel the equivalent resistance of the combination is
(a) \( R_1 + R_2 \)
(b) \( R_1 – R_2 \)
(c) \( \frac{R_1 R_2}{R_1 + R_2} \)
(d) \( \frac{R_1 + R_2}{R_1 R_2} \)
Answer: (c) \( \frac{R_1 R_2}{R_1 + R_2} \)

Question. The equivalent resistance of the resistors connected in parallel is
(a) greater than the greatest resistance
(b) smaller than the smallest resistance
(c) sum of all the resistance
(d) multiple of all the resistance
Answer: (b) smaller than the smallest resistance

Question. Magnitude of current in different branches of the parallel combination is
(a) same in each branch
(b) different in different branches
(c) divides as per number of branches
(d) none of the options
Answer: (b) different in different branches

Question. The total current in parallel combination of three resistors is
(a) \( I = I_1 + I_2 + I_3 \)
(b) \( I = \frac{I_1 + I_2}{I_3} \)
(c) \( I = (I_1 + I_2) \times I_3 \)
(d) \( I = I_1 + I_2 – I_3 \)
Answer: (a) \( I = I_1 + I_2 + I_3 \)

Question. To get \( 2 \text{ } \Omega \) resistance, using only \( 6 \text{ } \Omega \) resistors, the number of them required is
(a) 2
(b) 3
(c) 4
(d) 6
Answer: (b) Three resistors of \( 6 \text{ } \Omega \) is required to get \( 2 \text{ } \Omega \) because resultant is less than individual resistance when connected in parallel.

Question. Two devices are connected between two points say A and B in parallel. The physical quantity that will remain the same between the two points is
(a) current
(b) voltage
(c) resistance
(d) none of the options
Answer: (b) In parallel combination voltage remains same across two points.

Question. The resistance of resistor is reduced to half of its initial value. If other parameters of the circuit remain unchanged, the amount of heat produced in the resistor will become
(a) four times
(b) two times
(c) half
(d) one fourth
Answer: (b) two times

Question. In a resistive circuit if the current is increased to two times, the percentage change in the amount of heat dissipated in the circuit would be:
(a) 400%
(b) 300%
(c) 200%
(d) 100%
Answer: (b) 300%

Question. Elements of electric heating devices, such as bread toasters and electric iron are generally made up of
(a) metal
(b) non-metal
(c) alloy
(d) tin
Answer: (c) alloy

Question. According to Joule’s law of heating, the heat produced in a resistor in time t is
(a) \( H = I^2Rt \)
(b) \( H = IR^2t \)
(c) \( H = V^2It \)
(d) All of the options
Answer: (a) \( H = I^2Rt \)

Question. Which of the following is used almost exclusively for filaments of electric lamp?
(a) Copper
(b) Silver
(c) Tungsten
(d) Titanium
Answer: (c) Tungsten

Question. Water boils in an electric kettle in 18 minutes after switching on. If the length of heating wire is decreased to 1/3rd of its initial value, then the same amount of water will boil with the same supply of voltage in
(a) 6 minutes
(b) 12 minutes
(c) 54 minutes
(d) 18 minutes
Answer: (a) 6 minutes

Question. 50 J heat is produced each second in a \( 2 \text{ } \Omega \) resistor. The potential difference across the resistor is
(a) 10 V
(b) 25 V
(c) 50 V
(d) 100 V
Answer: (a) 10 V

Question. An electric fuse is based on
(a) the chemical effect of current
(b) the magnetic effect of current
(c) the heating effect of current
(d) none of the options
Answer: (c) the heating effect of current

Question. The fuse wire should have a
(a) low melting point
(b) high resistance
(c) high melting point
(d) both (a) and (b)
Answer: (d) both (a) and (b)