## Explain the following

[question] Question. Explain the following : (1)Why is tungsten used almost exclusively for filament of incandescent lamps ? (2)Why are the conductors of electric heating devices, such as toasters and electric irons, made of an alloy rather than a pure metal ? (3)Why is the series arrangement not used for domestic circuits ? (4)How does the resistance of a wire vary with its cross-sectional area ? (5)Why are copper and aluminium wires usually employed for electricity transmission ? [/question] [...

## An electric heater of resistance $8 \Omega$ draws $15 \mathrm{~A}$ from the service mains for 2 hours.

[question] Question. An electric heater of resistance $8 \Omega$ draws 15 A from the service mains for 2 hours. Calculate the rate at which heat is developed in the heater. [/question] [solution] solution: Here, $\mathrm{I}=15 \mathrm{~A}, \mathrm{R}=8 \Omega, \mathrm{t}=2 \mathrm{~h}$ Rate at which heat is developed, i.e, electric power, $\mathrm{P}=\mathrm{I}^{2} \mathrm{R}=(15)^{2} \times 8=1800 \mathrm{~W}$ [/solution]...

## Which uses more energy,

[question] Question. Which uses more energy, a $250 \mathrm{~W}$ TV set in $1 \mathrm{~h}$, or a $1200 \mathrm{~W}$ toaster in 10 minutes ? [/question] [solution] solution: Energy used by $250 \mathrm{~W}$ TV set in $1 \mathrm{~h}=250 \times 1=250 \mathrm{Wh}$ Energy used by $1200 \mathrm{~W}$ toaster in $10 \mathrm{~min}$. (i.e., $1 / 6 \mathrm{~h})=1200 \times(1 / 6)=200 \mathrm{Wh}$ Thus, a $250 \mathrm{~W}$ TV set uses more energy in $1 \mathrm{~h}$ than a $1200 \mathrm{~W}$ toaster in 10 mi...

## Two lamps, one rated 100 W at 220 V

[question] Question. Two lamps, one rated $100 \mathrm{~W}$ at $220 \mathrm{~V}$, and the other $60 \mathrm{~W}$ at $220 \mathrm{~V}$, are connected in parallel to the electric mains supply. What current is drawn from the line if the supply voltage is 220 V ? [/question] [solution] solution: Resistance of first lamp, $R_{1}=\frac{V^{2}}{P}=\frac{(220)^{2}}{100}$ resistance of the second lamp, $\mathrm{R}_{2}=\frac{\mathrm{V}^{2}}{\mathrm{P}}=\frac{(220)^{2}}{60}$ Since the two lamps are connecte...

## Compare the power used in the $2 \Omega$ resistor in cach of the following circuits:

[question] Question. Compare the power used in the $2 \Omega$ resistor in each of the following circuits: (i) a $6 \mathrm{~V}$ battery in series with $1 \Omega$ and $2 \Omega$ resistors, and (ii) a $4 \mathrm{~V}$ battery in parallel with $12 \Omega$ and $2 \Omega$ resistors. [/question] [solution] solution: (i) Since $6 \mathrm{~V}$ battery is in series with $1 \Omega 2$ and $2 \Omega \Omega$ resistors, current in the circuit, $I=\frac{6}{1+2}=\frac{6}{3}=2 \mathrm{~A}$ Power used in $2 \Omega...

## Several electric bulbs designed to be used on a 220 V electric supply line,

[question] Question. Several electric bulbs designed to be used on a 220 V electric supply line, are rated 10 W. How many lamps can be connected in parallel with each other across the two wires of 220 V line, if the maximum allowable current is 5 A ? [/question] [solution] solution: Resistance of each bulb, $R=\frac{V^{2}}{P}=\frac{(220)^{2}}{10}=4840 \Omega$ Total resistance in the circuit, $\mathrm{R}_{*}=\frac{220}{5}=44 \Omega$ Let $\mathrm{n}$ be the number of bulb (each of resistance $\mat...

## Show how you would connect three resistors,

[question] Question. Show how you would connect three resistors, each of resistance $6 \Omega$, so that the combination has a resistance of (i) $9 \Omega$ (ii) $2 \Omega$. [/question] [solution] solution: (i) In order to get a resistance of $9 \Omega$ from three resistors, we connect two $6 \Omega$ resistors in parallel and this parallel combination in series with the third $6 \Omega$ resistor as shown in fig. Two $6 \Omega$ resistors are in parallel, their equivalent resistance is, $\mathrm{R}_...

## How many $176 \Omega$ resistors (in parallel) are

[question] Question. How many $176 \Omega$ resistors (in parallel) are required to carry $5 \mathrm{~A}$ in $220 \mathrm{~V}$ line? [/question] [solution] solution: Here, $I=5 \mathrm{~A}, \mathrm{~V}=220 \mathrm{~V} .$ Resistance required in the circuit, $\mathrm{R}=\frac{\mathrm{V}}{\mathrm{I}}=\frac{220 \mathrm{~V}}{5 \mathrm{~A}}=44 \Omega$ Resistance of each resistor, $\mathrm{r}=176 \Omega$ If $\mathrm{n}$ resistors, each of resistance $\mathrm{r}$, are connected in parallel to get the req...

## A battery of 9 V is connected with resistors

[question] Question. A battery of $9 \mathrm{~V}$ is connected with resistors of $0.2 \Omega, 0.3 \Omega, 0.4 \Omega, 0.5 \Omega$ and $12 \Omega$ in series. How much current would flow through the $12 \Omega$ resistor? [/question] [solution] solution: Since all the resistors are in series, equivalent resistance, $R_{\varepsilon}=0.2+0.3+0.4+0.5+12=13.4 \Omega$ Current, $\mathrm{I}=\frac{\mathrm{V}}{\mathrm{R}_{2}}=\frac{9}{13.4}=0.67 \mathrm{~A}$ In series, same current (I) flows through all the...

## When a 12 V battery is connected across an

[question] Question. When a 12 V battery is connected across an unknown resistor, there is a current of 2.5 mA in the circuit. Find the value of the resistance of the resistor. [/question] [solution] solution: Here, $\mathrm{V}=12 \mathrm{~V}, \mathrm{I}=2.5 \mathrm{~mA}=2.5 \times 10^{-3} \mathrm{~A}$ Resistance of the resistor, $\mathrm{R}=\frac{\mathrm{V}}{\mathrm{l}}=\frac{12}{2.5 \times 10^{-3}}$ $=4800 \Omega=4.8 \mathrm{k} \Omega$ [/solution]...

## The values of current,

[question] Question. The values of current, I, flowing in a given resistor for the corresponding values of potential difference, $V$, across the resistor are given below : I (ampere): $\quad 0.5 \quad 1.0 \quad 2.0 \quad 3.0 \quad 4.0$ $\begin{array}{lllllll}\text { V (volt) } & : & 1.6 & 3.4 & 6.7 & 10.2 & 13.2\end{array}$ Plot a graph between $\mathrm{V}$ and $\mathrm{I}$ and calculate the resistance of the resistor. [/question] [solution] solution: The V-I graph is as shown in fig. Here, the ...

## A copper wire has a diameter of 0.5 mm

[question] Question. A copper wire has a diameter of $0.5 \mathrm{~mm}$ and a resistivity of $1.6 \times 10^{-6} \mathrm{ohm} \mathrm{cm}$. How much of this wire would be required to make a 10 ohm coil? How much does the resistance change if the diameter is doubled? [/question] [solution] solution: We are given that, diameter of the wire, $D=0.5 \mathrm{~mm}=0.5 \times 10^{-3} \mathrm{~m}$ Radius $\mathrm{r}=\frac{\mathrm{D}}{2}=\frac{0.5 \times 10^{-3}}{2}=2.5 \times 10^{-4} \mathrm{~m}$ Resist...

## How is voltmeter connected in the circuit

[question] Question. How is voltmeter connected in the circuit to measure potential difference between two points? [/question] [solution] solution: A voltmeter is always connected in parallel across the points between which the potential difference is to be determined. [/solution]...

## Two conducting wires of the same material

[question] Question. Two conducting wires of the same material and of equal lengths and equal diameters are first connected in series and then in parallel in an electric circuit. The ratio of the heat produced in series and parallel combinations would be (1) 1 : 2 (2) 2 : 1 (3) 1 : 4 (4) 4 : 1 [/question] [solution] solution: Since both the wires are made of the same material and have equal lengths and equal diameters, they have the same resistance. Let it be R. When connected in series, their e...

## An electric bulb is rated 220 V and 100 W

[question] Question. An electric bulb is rated 220 V and 100 W. When it is operated on 110 V, the power consumed will be: (1) 100 W (2) 75 W (3) 50 W (4) 25 W [/question] [solution] solution: Resistance of the electric bulbs, $R=\frac{V^{2}}{P}$\ $\left(P=\frac{V^{2}}{R}\right)$ or $\mathrm{R}=\frac{(220)^{2}}{100}=484 \Omega$ Power consumed by the bulb when it is operated at 110 V is given by $\mathrm{P}^{\prime}=\frac{\mathrm{V}^{2}}{\mathrm{R}}=\frac{(110)^{2}}{484}=\frac{110 \times 110}{484}...

## Which of the following terms does not represent electrical power in a circuit ?

[question] Question. Which of the following terms does not represent electrical power in a circuit ? (1) $I^{2} R$ (2) $\mathrm{IR}^{2}$ (3) VI (4) $\mathrm{V}^{2} / \mathrm{R}$ [/question] [solution] solution: Electrical power, $\mathrm{P}=\mathrm{VI}=(\mathrm{IR}) \mathrm{I}=\mathrm{I}^{2} \mathrm{R}$ $\mathrm{P}=\mathrm{V} \mathrm{I}=\mathrm{V}\left(\frac{\mathrm{V}}{\mathrm{R}}\right)=\frac{\mathrm{V}^{2}}{\mathrm{R}}$ Obviously, $\mathrm{IR}^{2}$ does not represent electrical power in a cir...

## A piece of wire of resistance R is cut into five equal parts.

[question] Question. A piece of wire of resistance $R$ is cut into five equal parts. These parts are then connected in parallel. If the equivalent resistance of this combination is $R^{\prime}$, then the ratio $R / R^{\prime}$ is (1) $\frac{1}{25}$ (2) $\frac{1}{5}$ (3) 5 (4) 25 [/question] [solution] solution: Resistance of each one of the five parts $=\frac{\mathrm{R}}{5}$ Resistance of five parts connected in parallel is given by $\frac{1}{\mathrm{R}^{\prime}}=\frac{1}{\mathrm{R} / 5}+\frac{1...

## An electric motor takes 5 A from a 220 V.

[question] Question. An electric motor takes 5 A from a 220 V. Determine the power and energy consumed in 2 hr. [/question] [solution] solution: Here, current, $\mathrm{I}=5 \mathrm{~A}$; potential difference, $\mathrm{V}=220 \mathrm{~V}$; time, $\mathrm{t}=2 \mathrm{hr}=2 \times 60 \times 60=7200 \mathrm{~s}$ Power, $\mathrm{P}=\mathrm{V} \times \mathrm{I}=220 \times 5=1100 \mathrm{~W}$ Energy consumed, $\mathrm{H}=\mathrm{V} \times \mathrm{I} \times \mathrm{t}=220 \times 5 \times 7200=7.92 \ti...

## What determines the rate at which energy

[question] Question. What determines the rate at which energy is delivered by a current ? [/question] [solution] solution: Electric power determines the rate at which energy is delivered by a current. [/solution]...

## An electric iron of resistance

[question] Question. An electric iron of resistance $20 \Omega$ takes a current of 5 A. Calculate the heat developed in $30 \mathrm{~s} .$ [/question] [solution] solution: Here, resistance, $R=20 \Omega$, current, $I=5 A$, time, $t=30 \mathrm{~s}$. Heat produced, $\mathrm{H}=\mathrm{I}^{2} \mathrm{R} \mathrm{t}=(5)^{2} \times 20 \times 30$ $=1.5 \times 10^{4} \mathrm{~J}$ [/solution]...

## Compute the heat generated while transferring

[question] Question. Compute the heat generated while transferring 96000 coulombs of charge in one hour through a potential difference of 50 V. [/question] [solution] solution: Here, charge, $\mathrm{Q}=96000 \mathrm{C} ;$ time, $\mathrm{t}=1 \mathrm{hr}$ potential difference, $\mathrm{V}=50 \mathrm{~V}$. Heat produced, $\mathrm{H}=\mathrm{V} \mathrm{I} \mathrm{t}=\mathrm{V} \times \mathrm{Q} \quad[\because \mathrm{Q}=\mathrm{I} \mathrm{t}]$ $=96000 \mathrm{C} \times 50 \mathrm{~V}=4.8 \times 10...

## Why does the cord of an electric heater

[question] Question. Why does the cord of an electric heater not glow while the heating element does ? [/question] [solution] solution: The cord of an electric heater is made of thick copper wire and has much lower resistance than the heating element. For the same current (I) flowing through the cord and the element, heat produced in the element is much more than that produced in the cord. As a result, the element becomes very hot and glows whereas the cord does not become hot and as such does n...

## What is (a) the highest,

[question] Question. What is (a) the highest, (b) the lowest total resistance that can be secured by combinations of four coils of resistances $4 \Omega, 8 \Omega, 12 \Omega, 24 \Omega$ ? [solution] solution: (a) The highest resistance is secured when all the resistors are connected in series. The equivalent resistance is given by $R_{g}=4 \Omega+8 \Omega+12 \Omega+24 \Omega=48 \Omega$ (2) The lowest resistance is secured when all the four coils are connected in parallel. The equivalent resistan...

## How can three resistors of resistances

[question] Question. How can three resistors of resistances $2 \Omega, 3 \Omega$, and $6 \Omega$ be connected to give a total resistance of (a) $4 \Omega$ (b) $1 \Omega$ ? [/question] [solution] solution: (a) To get a total resistance of $4 \Omega$ from resistors of resistances $2 \Omega, 3 \Omega$ and $6 \Omega$, the resistors are joined as shown below. The resistors having resistances $3 \Omega$ and $6 \Omega$ are connected in parallel. This combination is connected in series with the resistor...

## What are the advantages of connecting electrical

[question] Question. What are the advantages of connecting electrical devices in parallel with the battery instead of connecting them in series. [/question] [solution] solution: (a)In case of devices in parallel, if one device gets damaged (or open), all others will work as usual as the whole circuit does not break. This is not so with the devices connected in series because when one device fails, the circuit breaks and all devices stop working. (b)Since potential difference across all devices i...

## Judge the equivalent resistance

[question] Question. Judge the equivalent resistance when the following are connected in parallel (a) $1 \Omega$ and $10^{6} \Omega$ (b) $1 \Omega, 10^{3} \Omega$ and $10^{6} \Omega$. [/question] [solution] solution: (a) Approx. $1 \Omega$ (slightly less than $1 \Omega$ ) as other one $\left(10^{6} \Omega\right)$ is very large as compared to $1 \Omega$. In parallel combination of resistors, the equivalent resistance is lesser than the least resistance (in this case, $1 \Omega$ ). (b)Again, resis...

## Redraw the circuit of Q. 1,

[question] Question. Redraw the circuit of Q. 1, putting in an ammeter to measure the current through the resistors and a voltmeter to measure the voltage across the 12 ohm resistor. What would be the readings in the ammeter and the voltmeter ? [/question] [solution] solution: Since all the three resistances are in series, total resistance in the circuit, $R=5+8+12=25 \Omega$ Current in the circuit, $\mathrm{I}=\frac{\mathrm{V}}{\mathrm{D}}=\frac{2+2+2}{25}=\frac{6}{25}=0.24 \mathrm{~A}$, thus, ...

## Draw a schematic diagram of a circuit consisting of a battery

[question] Question. Draw a schematic diagram of a circuit consisting of a battery of three cells of $2 \mathrm{~V}$ each, a 5 ohm resistor, an $8 \mathrm{ohm}$ resistor, and a $12 \mathrm{ohm}$ resistor, and a plug key, all connected in series. [/question] [solution] solution: [/solution]...

## (a) Which among iron and mercury is a better conductor?

[question] Question. (a) Which among iron and mercury is a better conductor? Given, $\rho_{\text {iron }}=10.0 \times 10^{-8} \Omega \mathrm{m}$ and $\rho_{\text {mercury }}=94.0 \times 10^{-8} \Omega \mathrm{m}$ (b) Which material is the best conductor ? [/question] [solution] solution: (a) Iron is a better conductor than mercury as resistivity $(\rho)$ for iron is less than that for mercury. (b) Silver is the best conductor because its resistivity $(\rho)$ is least. [/solution]...

## Why are coils of electric toasters and electric irons

[question] Question. Why are coils of electric toasters and electric irons made of an alloy rather than a pure metal ? [/question] [solution] solution: This is because (i) resistivity of an alloy is generally higher than that of pure metals (ii) an alloy does not oxidise at high temperatures. [/solution]...

## Let the resistance of an electrical component remain constant

[question] Question. Let the resistance of an electrical component remain constant while the potential difference across the two ends of the component decrease to half its former value. What change will occur in the current through it ? [/question] [solution] solution: We know that $I=V / R$, when potential difference becomes $V / 2$, and resistance remains constant, then, current becomes $1 / 2$ of its former value. [/solution]...

## Does current flow more easily through a thick wire

[question] Question. Does current flow more easily through a thick wire or a thin wire of the same material when connected to the same source ? Why ? [/question] [solution] solution: The current flows more easily through a thick wire than through a thin wire. This is because, the resistance R of a thick wire (large area of cross-section) is less than that of a hin wire (small area of cross-section) as $\mathrm{R} \propto \frac{1}{\mathrm{~A}}$. [/solution]...

## On what factors does the resistance

[question] Question. On what factors does the resistance of a conductor depend ? [/question] [solution] solution: The resistance $(R)$ of a conductor depends upon (1) Its length $(\ell): \mathrm{R} \propto \ell$ (2) Its cross-sectional area (A): $R \propto \frac{1}{A}$ (3) Nature of material i.e., resistivity $(\rho)$ of its material: $R \propto \rho$ (4) Temperature: more the temperature, more will be its resistance. [/solution]...

## How much energy is given to each coulomb

[question] Question. How much energy is given to each coulomb of charge passing through a 6 V battery ? [/question] [solution] solution: Work done, $\mathrm{W}=\mathrm{QV}$ where $\mathrm{Q}=1 \mathrm{C} ; \mathrm{V}=6 \mathrm{~V}$ $\mathrm{W}=1 \mathrm{C} \times 6 \mathrm{~V}=\mathbf{6} \mathbf{J}$ [/solution]...

## What is meant by saying that the potential

[question] Question. What is meant by saying that the potential difference between two points is 1 V ? [/question] [solution] solution: Potential difference between two points is 1 volt if 1 joule of work is done to carry a charge of 1 coulomb from one point to the other. [/solution]...

## Name a device that helps to maintain a potential

[question] Question. Name a device that helps to maintain a potential difference across a conductor. [/question] [solution] solution: A battery can be used to maintain a potential difference across a conductor. [/solution]...

## Calculate the number of electrons constituting

[question] Question. Calculate the number of electrons constituting one coulomb of charge. [/question] [solution] solution: Number of electrons constituting 1 coulomb is given by, $\mathrm{n}=\frac{\mathrm{Q}}{\mathrm{e}}$ Where, $\mathrm{Q}=1 \mathrm{C}$ and $\mathrm{e}=$ charge of a single electron $=1.6 \times 10^{-19} \mathrm{C}$ or $\mathrm{n}=\frac{1 \mathrm{C}}{1.610^{-19} \mathrm{C}}=6.24 \times 10^{18}$ electrons. [/solution]...

## Define the SI unit of current.

[question] Question. Define the SI unit of current. [/question] [solution] solution: The SI unit of current is ampere (A). Current flowing through a conductor is said to be 1 ampere if 1 coulomb of charge flows through it in 1 second. [/solution]...

## What does an electric circuit mean ?

[question] Question. What does an electric circuit mean ? [/question] [solution] solution: An electric circuit is a closed and continuous path consisting of many devices like resistors, electric bulbs, etc. through which an electric current flows. [/solution]...