CBSE Class 10 Science — Electricity

(a) The resistance of a wire of 0.01 cm radius and 1.0 cm length is $7\Omega$. Calculate its resistivity. (b) An electric heater is rated 220 V; 11 A. Calculate the power consumed if the heater is operated at 200 V.

(a) Why does an electric bulb become dim when an electric heater in a parallel circuit is switched ON? (b) How would you connect three resistors, each of resistance $8\,\Omega$, so that the equivalent resistance of the combination is $12\,\Omega$? Draw the diagram of the combination and justify your answer.

(a) Why does an electric bulb become dim when an electric heater in parallel circuit is switched ON? (b) How to connect three resistors each of resistance 8 Ω, so that the equivalent resistance of the combination is 12 Ω? Draw diagram of the combination and justify your answer.

Three students Shweta, Ayesha and Samridhi were performing an experiment to understand the factors on which the resistance of a conductor depends. Each one of them completed an electric circuit with the help of a cell, an ammeter, a plug key and wire. Shweta put a nichrome wire of length 'l' in the circuit and after plugging the key, noted the current in the ammeter. Ayesha put a nichrome wire of the same thickness but twice the length, i.e. '2l', in the circuit and after plugging the key, noted the current in the ammeter. Samridhi took a copper wire of length 'l' and the same thickness in the circuit and after plugging the key, noted the current in the ammeter. (a) If the ammeter reading is X ampere with nichrome wire of length 'l', then what will be the ammeter reading if the length of the nichrome wire is doubled with the same area of cross-section? (b) What happens to the ammeter reading if the area of cross-section of the nichrome wire is doubled, keeping the length of the wire 'l' the same? (c) Define 'resistivity'. Write its SI unit. Compare the resistivity of an alloy with its constituent metals. OR (c) Give reason: (i) Tungsten is used almost exclusively for making the filament of electric lamps. (ii) Conductors of bread-toasters are made of an alloy rather than a pure metal.

Three students Shweta, Ayesha and Samridhi were performing an experiment to understand the factors on which the resistance of a conductor depends. Each one of them completed electric circuit with the help of a cell, an ammeter, a plug key and wire. Shweta put nichrome wire of length 'l' in the circuit. Ayesha put nichrome wire of same thickness but twice the length i.e. '2l'. Samridhi took copper wire of length 'l' and same thickness. (a) If the ammeter reading is X ampere with nichrome wire of length 'l', then what will be the ammeter reading if the length of nichrome wire is doubled with same area of cross-section? (b) What happens to the ammeter reading if the area of cross-section of nichrome wire is doubled, keeping the length of wire 'l' the same? (c) Define 'resistivity'. Write its SI unit. Compare the resistivity of an alloy with its constituents metals. OR (c) Give reason: (i) Tungsten is used almost exclusively for making the filament of electric lamps. (ii) Conductors of bread-toasters are made of an alloy rather than a pure metal.

(a) (i) Due to change in length and area of cross-section of a conductor, resistance of conductor changes while resistivity does not change. Why? (ii) Conductors of electric toasters and electric iron are made of an alloy rather than a pure metal. Why? (iii) Define the S.I. unit of electric current. OR (b) (i) How many bulbs of resistance $8\Omega$ each should be connected in parallel combination to draw a current of $2\mathrm{A}$ from a battery of $4\mathrm{V}$? (ii) Name the device used for measuring electric current. How is it connected in a circuit? (iii) State Joule's law of heating.

(A) (i) List any two features of the electric current used in the houses of India. (ii) Write any two differences between direct current and alternating current. (iii) How will you identify the live wire and the neutral wire in a domestic electric circuit? OR (B) (i) Why is fuse an important component in our electric circuits? (ii) Distinguish between overloading and short-circuiting of a circuit. (iii) Giving reason, explain what type of materials are used in fuse wires.

A piece of wire of resistance 'R' is cut lengthwise into three identical parts. These parts are then connected in parallel. If the equivalent resistance of this combination is R', then the value of R/R' is :

An electric bulb is rated $220\text{ V}; 11\text{ W}$. The resistance of its filament when it glows with a power supply of $220\text{ V}$ is :

A wire of length 'l' is gradually stretched so that its length increases to $3l$. If its original resistance is $R$, then its new resistance will be :

An electric bulb is connected to a power supply of $220~\mathrm{V}$. If the current drawn by the bulb from the supply is $500~\mathrm{mA}$, the power of the bulb is:

The minimum number of identical bulbs of rating $4\text{ V}; 6\text{ W}$, that can work safely with desired brightness, when connected in series with a $240\text{ V}$ mains supply is :

Four identical resistors of $12\ \Omega$ each are connected in series to form a square ABCD as shown in the figure. The resistance of the network between the two points 1 and 2 is:

Assertion (A): In the common domestic circuits the earth wire is connected to a metallic plate buried deep inside the earth. Reason (R): Earth wire ensures that any leakage of current to the metallic body of the appliance keeps its potential to that of the earth, so the user may not get a severe electric shock.

Assertion (A): Nichrome is an alloy which is commonly used in electrical heating devices such as electric irons, toasters, etc. Reason (R): The resistivity of nichrome is high and its resistance decreases with increase in temperature.

(A) State two applications of Joule's heating in domestic electric circuit. OR (B) (a) Establish the relationship between the commercial unit of electric energy and the SI unit of electric energy. (b) Determine the total resistance of the parallel combination of three resistances of $2 \Omega$, $4 \Omega$ and $6 \Omega$.

(a) A wire of resistance R is cut into three equal parts. If these three parts are then joined in parallel, calculate the total resistance of the combination so formed. OR (b) Define electric power. When do we say that the power consumed in an electric circuit is 1 watt?

An electric kettle is rated 230 V; 1000 W. Calculate the resistance of its heating element when in operation.

An electric kettle is rated $750\ \mathrm{W}$; $220\ \mathrm{V}$. Can this kettle be used in a circuit which has a fuse of current rating $3\ \mathrm{A}$? Give reason for your answer.

Three resistors of $2\ \Omega$, $3\ \Omega$ and $6\ \Omega$ are connected in (i) series, and (ii) parallel. Draw the arrangements of the resistors and find the equivalent resistance of each arrangement.

The resistance of a wire of $0.01 cm$ radius is 7 ohms. If the resistivity of the material of the wire is $44 \times 10^{-6} ohm$ meter, calculate the length of the wire.

The electrical resistivity of three materials A, B and C at $20^{\circ}C$ is given below: Material | Resistivity (Ω m) A | $10^{17}$ B | $44 \times 10^{-6}$ C | $1.62 \times 10^{-8}$ (i) Classify these materials as conductor, alloy and insulator. (ii) Give one example of each of these materials and state one use of each material in the design of an electrical appliance say an electric stove or an electric iron.

(a) Write the relationship between resistivity and resistance of a cylindrical conductor of length $l$ and area of cross-section A. Hence derive the SI unit of resistivity. (b) Why are alloys used in electrical heating devices?

(a) Explain the statement "Potential difference between two points is 1 volt". (b) What do the symbols given below represent in an electric circuit? Write one function of each.

(a) "The third wire of earth connection is very important in domestic electric appliances." Justify this statement. (b) List two precautions to be taken to avoid the overloading of domestic electric circuits.

As shown in the diagram, an electric circuit consisting of an ammeter, a voltmeter, 4 cells of $1\cdot 5\ \mathrm{V}$ each, a plug key with a gap XY was set up. Voltmeter and ammeter readings were recorded in the observation table for four arrangements as given below : Arrangement No. 1 - only resistor $R_1$ in gap XY Arrangement No. 2 - only resistor $R_2$ in gap XY Arrangement No. 3 - Resistors $R_1$ and $R_2$ in series in gap XY Arrangement No. 4 - Resistors $R_1$ and $R_2$ in parallel in gap XY Based on the observations, four V-I graphs A, B, C and D as shown in figure were drawn. Study these graphs. (a) Which one of the graphs represents the series combination of $R_1$ and $R_2$ ? [1] (b) Which one of these graphs represents the parallel combination of $R_1$ and $R_2$ ? [1] (c) (i) Show an arrangement of three resistors, each of resistance $10\ \Omega$, so that the combination has a resistance of $15\ \Omega$. Give justification for your answer. [2] OR (c) (ii) A battery of $6\ \mathrm{V}$ is connected with a series combination of five resistors of $0\cdot 1\ \Omega$, $0\cdot 2\ \Omega$, $0\cdot 3\ \Omega$, $0\cdot 4\ \Omega$ and $0\cdot 5\ \Omega$. How much current would flow through the $0\cdot 3\ \Omega$ resistor? Justify your answer. [2]

In our homes, we receive the supply of electric power through a main supply also called mains, either supported through overhead electric poles or by underground cables. In our country the potential difference between the two wires (live wire and neutral wire) of this supply is $220\ V$. (a) Write the colours of the insulation covers of the line wires through which supply comes to our homes. [1] (b) What should be the current rating of the electric circuit ($220\ V$) so that an electric iron of $1\ kW$ power rating can be operated? [1] (c) (i) What is the function of the earth wire? State the advantage of the earth wire in domestic electric appliances such as electric iron. [2] OR (c) (ii) List two precautions to be taken to avoid electrical accidents. State how these precautions prevent possible damage to the circuit/appliance. [2]

In case of four wires of same material, the resistance will be minimum if the diameter and length of the wire respectively are

An electric iron of resistance $20 \Omega$ draws a current of $5 \mathrm{~A}$. The heat developed in the iron in 30 seconds is :

The maximum resistance of a network of five identical resistors of $\frac{1}{5} \Omega$ each can be -

Assertion (A): Electrons move from lower potential to higher potential in a conductor. Reason (R): A dry cell maintains electric potential difference across the ends of a conductor.

(A) Show how you would connect three resistors each of resistance $6\Omega$, so that the combination has a resistance of $9\Omega$. Also justify your answer. OR (B) In the given circuit calculate the power consumed in watts in the resistor of $2\Omega$ :

An electric source can supply a charge of 500 coulomb. If the current drawn by a device is $25 \mathrm{mA}$, find the time in which the electric source will be discharged completely.

Two wires A and B of same material, having same lengths and diameters $0.2 \mathrm{mm}$ and $0.3 \mathrm{mm}$ respectively, are connected one by one in a circuit. Which one of these two wires will offer more resistance to the flow of current in the circuit? Justify your answer.

(a) (i) The potential difference across the two ends of a circuit component is decreased to one-third of its initial value, while its resistance remains constant. What change will be observed in the current flowing through it? Name and state the law which helps us to answer this question. (ii) Draw a schematic diagram of a circuit consisting of a battery of four $1.5 \mathrm{~V}$ cells, a $5 \Omega$ resistor, a $10 \Omega$ resistor and a $15 \Omega$ resistor and a plug key, all connected in series. Now find (I) the electric current passing through the circuit, and (II) potential difference across the $10 \Omega$ resistor when the plug key is closed. OR (b) (i) When is the potential difference between two points said to be 1 volt? (ii) A copper wire has a diameter of $0.2 \mathrm{~mm}$ and resistivity of $1.6 \times 10^{-8} \Omega \mathrm{~m}$. What will be the length of this wire to make its resistance $14 \Omega$? How much does the resistance change, if the diameter of the wire is doubled?

(A) (i) Define electric power. Express it in terms of potential difference (V) and resistance (R). (ii) An electric oven is designed to work on the mains voltage of 220 V. This oven consumes 11 units of electrical energy in 5 hours. Calculate: (a) power rating of the oven (b) current drawn by the oven (c) resistance of the oven when it is red hot OR (B) (i) Write the relation between resistance R and electrical resistivity $\rho$ of the material of a conductor in the shape of cylinder of length $l$ and area of cross-section A. Hence derive the SI unit of electrical resistivity. (ii) The resistance of a metal wire of length $3\mathrm{m}$ is $60\Omega$ . If the area of cross-section of the wire is $4\times 10^{-7}\mathrm{m}^2$ , calculate the electrical resistivity of the wire. (iii) State how would electrical resistivity be affected if the wire (of part 'ii') is stretched so that its length is doubled. Justify your answer.

When electric current flows in a purely resistive circuit electrical energy gets fully converted into heat energy. The amount of heat produced (H) in the circuit is found to be directly proportional to (i) the square of current ($I^2$) (ii) the resistance (R) of the conductor and (iii) the time (t) for which current flows. In other words $\mathrm{H} = \mathrm{I}^2\mathrm{Rt}$. Electrical devices such an electric fuse, electric heater, electric iron etc. are all based on this effect called heating effect of electric current. (a) List two properties of heating elements. (b) List two properties of electric fuse. (c) Name the principle on which an electric fuse works. Explain how a fuse wire is capable of saving electrical appliances from getting damaged due to accidently produced high currents. OR (c) The power of an electric heater is 1100 W. If the potential difference between the two terminals of the heater is 220 V, find the current flowing in the circuit. What will happen to an electric fuse of rating 5 A connected in this circuit?

Study the following circuit : On the basis of this circuit, answer the following questions : (a) Find the value of total resistance between the points A and B. (b) Find the resistance between the points B and C. (c) (i) Calculate the current drawn from the battery, when the key is closed. OR (c) (ii) In the above circuit, the $16\Omega$ resistor or the parallel combination of two resistors of $8\Omega$, which one of the two will have more potential difference across its two ends? Justify your answer.

Two LED bulbs of $12W$ and $6W$ are connected in series. If the current through $12W$ bulb is $0.06A$ the current through $6W$ bulb will be :

The expressions that relate (i) Q, I and t and (ii) Q, V and W respectively are (Here the symbols have their usual meanings):

If four identical resistors, of resistance 8 ohm, are first connected in series so as to give an effective resistance $R_s$, and then connected in parallel so as to give an effective resistance $R_p$, then the ratio $R_s/R_p$ is

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 the resistor, the :

An electric kettle consumes 1 kW of electric power when operated at 220 V. The minimum rating of the fuse wire to be used for it is

The resistance of a resistor is reduced to half of its initial value. If other parameters of the electrical circuit remain unaltered, the amount of heat produced in the resistor will become :

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 :

Let the resistance of an electrical device remain constant, while the potential difference across its two ends decreases to one fourth of its initial value. What change will occur in the current through it? State the law which helps us in solving the above stated question.

V-I graph for two conducting wires A and B are as shown. If both wires are of the same length and same diameter, which of the two is made of a material of high resistivity? Give reasons to justify your answer.

Explain the meaning of overloading of an electrical circuit. List two possible causes due to which overloading may occur in household circuits. Write one preventive measure that should be taken to avoid overloading of domestic circuits.

(a) (i) What is meant by resistance of a conductor? Define its SI unit. (ii) List two factors on which the resistance of a rectangular conductor depends. (iii) How will the resistance of a wire be affected if its (1) length is doubled, and (2) radius is also doubled? Give justification for your answer. OR (b) In an electric circuit three bulbs of 100 W each are connected in series to a source. In another circuit set of three bulbs of the same wattage are connected in parallel to the same source. (i) Will the bulb in the two circuits glow with the same brightness? Justify your answer. (ii) Now, let one bulb in both the circuits get fused. Will the rest of the bulbs continue to glow in each circuit? Give reason for your answer.

(a) An electric iron consumes energy at a rate of 880 W when heating is at the maximum rate and 330 W when the heating is at the minimum. If the source voltage is 220 V, calculate the current and resistance in each case. (b) What is heating effect of electric current? (c) Find an expression for the amount of heat produced when a current passes through a resistor for some time.

(i) How is electric current related to the potential difference across the terminals of a conductor ? Draw a labelled circuit diagram to verify this relationship. (ii) Why should an ammeter have low resistance ? (iii) Two V - I graphs A and B for series and parallel combinations of two resistors are as shown. Giving reason state which graph shows (a) series, (b) parallel combination of the resistors.

(a) State Ohm's Law. Represent it mathematically. (b) Define 1 ohm. (c) What is the resistance of a conductor through which a current of $0.5\text{ A}$ flows when a potential difference of $2\text{ V}$ is applied across its ends ?

(a) List the factors on which the resistance of a uniform cylindrical conductor of a given material depends. (b) The resistance of a wire of $0.01\text{ cm}$ radius is $10\Omega$. If the resistivity of the wire is $50 \times 10^{-8}\Omega\text{ m}$, find the length of this wire.

(a) A student wants to use an electric heater, an electric bulb and an electric fan simultaneously. How should these gadgets be connected with the mains? Justify your answer giving three reasons. (b) What is an electric fuse? How is it connected in a circuit?

OR (a) What is the meaning of electric power of an electrical device? Write its SI unit. (b) An electric kettle of $2\text{ kW}$ is used for $2\text{ h}$. Calculate the energy consumed in (i) kilowatt hour and (ii) joules.

An electric motor rated 1100 W is connected to 220 V mains. Find: (i) The current drawn from the mains, (ii) Electric energy consumed if the motor is used for 5 hours daily for 6 days. (iii) Total cost of energy consumed if the rate of one unit is ₹5. OR Study the following circuit and find: (i) Effective resistance of the circuit (ii) Current drawn from the battery (iii) Potential difference across the $5\Omega$ resistor

The maximum resistance which can be made using four resistors each of $2\Omega$ is

The values of mA and $\mu A$ are

A cylindrical conductor of length 'l' and uniform area of cross section 'A' has resistance 'R'. The area of cross section of another conductor of same material and same resistance but of length '2l' is

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 student plots V-I graphs for three samples of nichrome wire with resistances $R_1$, $R_2$ and $R_3$. Choose from the following the statement that holds true for this graph.

The maximum resistance which can be made using four resistors each of resistance $\frac{1}{2} \Omega$ is

If a person has five resistors each of value $\frac{1}{5} \Omega$, then the maximum resistance he can obtain by connecting them is (A) $1 \Omega$ (B) $5 \Omega$ (C) $10 \Omega$ (D) $25 \Omega$ OR The resistance of a resistor is reduced to half of its initial value. In doing so, if other parameters of the circuit remain unchanged, the heating effects in the resistor will become

OR Two bulbs of $100\text{ W}$ and $40\text{ W}$ are connected in series. The current through the $100\text{ W}$ bulb is $1\text{ A}$. The current through the $40\text{ W}$ bulb will be:

At the time of short circuit, the electric current in the circuit:

Assertion (A): At high temperatures, metal wires have a greater chance of short circuiting. Reason (R): Both resistance and resistivity of a material vary with temperature.

Assertion (A): Alloys are commonly used in electrical heating devices like electric iron and heater. Reason (R): Resistivity of an alloy is generally higher than that of its constituent metals but the alloys have low melting points than their constituent metals.

A V-I graph for a nichrome wire is given below. What do you infer from this graph? Draw a labelled circuit diagram to obtain such a graph.

(a) Write the mathematical expression for Joule's law of heating. (b) Compute the heat generated while transferring $96000\text{ coulomb}$ of charge in two hours through a potential difference of $40\text{ V}$.

(a) Find the ratio of resistances of two copper rods X and Y of lengths 30 cm and 10 cm respectively and having radii 2 cm and 1 cm respectively. (b) A current of 500 mA flows in a series circuit containing an electric lamp and a conductor of 10Ω when connected to 6V battery. Find the resistance of the electric lamp.

(a) For the combination of resistors shown in the following figure, find the equivalent resistance between M & N. (b) State Joule's law of heating. (c) Why we need a 5 A fuse for an electric iron which consumes 1 kW power at 220 V? (d) Why is it impracticable to connect an electric bulb and an electric heater in series?

Draw a schematic diagram of a circuit consisting of a battery of 3 cells of $2\text{ V}$ each, a combination of three resistors of $10\Omega$, $20\Omega$ and $30\Omega$ connected in parallel, a plug key and an ammeter, all connected in series. Use this circuit to find the value of the following: (a) Current through each resistor (b) Total current in the circuit (c) Total effective resistance of the circuit OR Two identical resistors, each of resistance $15\Omega$, are connected in (i) series, and (ii) parallel, in turn to a battery of $6\text{ V}$. Calculate the ratio of the power consumed in the combination of resistors in each case.

(a) Two lamps rated $100 \text{ W}$, $220 \text{ V}$ and $10 \text{ W}$, $220 \text{ V}$ are connected in parallel to $220 \text{ V}$ supply. Calculate the total current through the circuit. (b) Two resistors X and Y of resistances $2 \Omega$ and $3 \Omega$ respectively are first joined in parallel and then in series. In each case the voltage supplied is $5 \text{ V}$. (i) Draw circuit diagrams to show the combination of resistors in each case. (ii) Calculate the voltage across the $3 \Omega$ resistor in the series combination of resistors.

Show how would you join three resistors, each of resistance 9 $\Omega$ so that the equivalent resistance of the combination is (i) 13.5 $\Omega$, (ii) 6 $\Omega$?

(a) Write Joule’s law of heating. (b) Two lamps, one rated 100 W; 220 V, and the other 60 W; 220 V, are connected in parallel to electric mains supply. Find the current drawn by two bulbs from the line, if the supply voltage is 220 V.

(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.

The values of current (I) flowing through a given resistor of resistance (R), for the corresponding values of potential difference (V) across the resistor are as given below: V (volts): 0.5, 1.0, 1.5, 2.0, 2.5, 3.0, 4.0, 5.0; I (amperes): 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.8, 1.0. Plot a graph between current (I) and potential difference (V) and determine the resistance (R) of the resistor.

A charge of $150\text{ C}$ flows through a wire in one minute. Find the electric current flowing through it.

A circuit has a line of $5\text{ A}$. How many lamps of rating $40\text{ W}$; $220\text{ V}$ can simultaneously run on this line safely?

The resistance of a wire of $0.01\text{ cm}$ radius is $10\ \Omega$. If the resistivity of the material of the wire is $50 \times 10^{-8}\ \Omega\cdot\text{m}$, find the length of the wire.

What is meant by resistance of a conductor? Name and define its SI unit. List the factors on which the resistance of a conductor depends. How is the resistance of a wire affected if: (i) its length is doubled, (ii) its radius is doubled?

In an experiment to find the equivalent resistance of a series combination of two resistances of $3\ \Omega$ and $4\ \Omega$ in the circuit diagram given. The circuit will give:

A student joined three resistances (two of $30\ \Omega$ in series, connected in parallel with a $20\ \Omega$ resistor) to a $7.5\text{ V}$ source. The current recorded by the ammeter (A) is:

A student while verifying Ohm's law calculated the value of resistance of the resistor for each set of observation. However, the values of resistance were slightly different from the actual value. Is his experiment wrong? Justify your answer.

Derive the expression for the heat produced due to a current 'I' flowing for a time interval 't' through a resistor 'R' having a potential difference 'V' across its ends. With which name is the relation known ? How much heat will an instrument of 12W produce in one minute if it is connected to a battery of 12V ? Or Explain with the help of a labelled circuit diagram how you will find the resistance of a combination of three resistors, of resistance $R_1$, $R_2$ and $R_3$, joined in parallel. Also mention how you will connect the ammeter and the voltmeter in the circuit when measuring the current in the circuit and the potential difference across one of the three resistors of the combination.