Class 10 Science | physics Long Questions for Electricity
Question 1. State Ohm's law. How can it be verified experimentally? Does it hold good in all conditions? Comment. Question 2. Express Joule's law of heating mathematically. Question 3. What is the resistance of 12 m wire having radius 2×10-4 m and resistivity 3.14×10-8 Ω-m. Solution
$R=\rho \frac {L}{A} $
Substituting all the values , we get
R=3Ω
Question 4. A 4Ω resistance wire is doubled on it. Calculate the new resistance of the wire. Solution
Here we consider wire doubled means to fold the length of wire. It means its length will get half and area of cross section will get double.
Let the resistance of the wire originally 'R' of length 'l' and area of cross-section 'A' with resistivity of material is 'ρ', Then
$R=\rho \frac {L}{A} =4$
When it is doubled, L1=L/2, A1=2A ,then
$R_1=\rho \frac {L/2}{2A} =\frac{1}{4} \rho \frac {L}{A}$ =1Ω
Question 5. An electric iron consumer's energy at a rate of 840 W when heating is at the maximum rate and 360 W when the heating is at the minimum,the voltage is 220 V. What are the current and the resistance in each case ? Solution
Case A : Maximum rate
P = 840W
V = 220V
We know
$P = VI$
or
$I = \frac {P}{V} = \frac {840}{220}$
I = 4 A
Now
$R = \frac {V}{I} = \frac {220}{4} = 55$ Ω
Case B: Minimum rate
P = 360W
V = 220V
Again
P = VI
or
$I = \frac {P}{V} = \frac {360}{220}$
I = 1.636 A
Now
$R = \frac {V}{I} = \frac {220}{1.636} = 134.45$ Ω
Question 6.
a.Define 1 volt. Express it in terms of SI unit of work and charge.
b. Calculate the amount of energy consumed in carrying a charge of 1 coulomb through a battery of 3 volts. Solution
a. One volt is defined as the the potential difference between two points in a current carrying conductor when one joule of work is done to move a charge of one coulomb from one point to another.
SI unit in terms of work and charge
1 volt= 1 joule / 1 coulomb
b. Q= 1 C ,V= 3 Volt
Workdone is given by
W = Q V = 3 Joule
Question 7. Write symbols of the following circuit elements:
(i) Battery
(ii) Ammeter
(iii) Voltmeter
State the role of these elements in an electric circuit. Solution
Battery -> It is used to supply electric current to the circuit
Ammeter -> It is used to measure electric current
Voltmeter -> It is used to measure Potential difference in the circuit
Question 8. What is meant by electrical resistance of a conductor? State how resistance of a conductor is affected when
(i) a low current passes through it for a short duration
(ii) a heavy current passes through it for about 30 seconds. Solution
Electric resistance of a conductor is the obstruction offered by the conductor to the flow of the current through it.
Electric resistance depends on lenght,area,resistivity and temperature.It does not depend on current. Infact current is determined by the voltage and resistance.
So Resistance would be same in both the cases
Question 9. How do we connect ammeter and voltmeter in an electric circuit? Draw a circuit diagram to justify your answer. What is likely to happen if the positions of these instruments are interchanged? Give reason. Solution
Ammeter is connected in series while voltmeter is connected in Parallel. If the are interchanged,incorrect reading will be specifoed
Question 10. A student has a resistance wire of 1 ohm. If the length of this wire is 50 cm, to what length he should stretch it uniformly so as to obtain a wire of 4 Ω resistance? Justify your answer. Solution
Let $\rho =a$
$R=\rho \frac {L}{A}$
$ 1 = a \frac {50}{A}$
or A= 50a
Now as Volume remains constant
$A_1L_1 = A_2 L_2$
$2500a= A_2 L_2$
Now
$R=\rho \frac {L}{A}$
$ 4 = a \frac {L}{A}$
$4 =a \frac {L}{2500a/L}$
$L^2 = 4 \times 2500$
$L^2 = 10000$
L=100 cm
So lenght should be doubled
Question 11. Calculate the resistivity of the material of a wire of length 1 m, radius 0.01 cm and of resistance 20 ohms. Solution
$R=\rho \frac {L}{A}$
$r = 0.01 cm = 1 \times 10^{-4} $ m
A = \pi r^2= 3.14 \times (1 \times 10^{-4} )^2 = 3.14 \times 10^{-8}$ m2
Question 12. The resistance per meter length of a wire is 10 Ω. If the resistivity of the material of the wire is 50×10-8 ohm meters, find the area of cross – section of the wire. Solution
Question 13. The resistance of a wire of 0.01 cm radius is 10 Ω. If the resistivity of the material of the wire is 50×10-8 ohm meters, find the length of the wire. Solution
Question 14. Show different ways in which three resistance of R ohm each may be connected in a circuit. In which case is the equivalent resistance of the combination:
(i) maximum
(ii) minimum Solution
When in Parallel , equivalent reistance
$ \frac {1}{R_eq}=\frac {1}{R} + \frac {1}{R} + \frac {1}{R}$
Req = R/3
When in Series, equivalent resistance
Req = 3R,
So when connected in series, maximum resistance is obtained and when connected in parallel ,minimum resistance is obtained
Important Question Question 15. Three resistors of 1 Ω, 2 Ω and 3 Ω are connected in parallel in a circuit. If 1 Ω resistor draw a current of 1 A, find the current through the other two resistors. Solution
Potential difference accross 1 Ω resistor = IR=1 V
Same potential difference will be there in other resistors also
So Current in 2 Ω resistor= 1/2 =.5 A
Similarly current in 3 Ω resistir= 1/3=.333 A
Question 16. When a resistor R is connected to a battery of 3 V, it draws a current of 1 ampere. find the value of R. If an identical resistor is connected in parallel with it, find the current that flows through the circuit?. Solution
By ohm law
$V=IR$
or $R = \frac {V}{I} = 3$Ω
Now when identical resistor is connected in parallel with it, effective resistance becomes
$ \frac {1}{R_{eq}}= \frac {1}{3} + \frac {1}{3}$
or $ R_{eq}= 1.5$ Ω
Now
$I = \frac {V}{R} = \frac {3}{1.5} =2 A$
Question 17. Derive an expression for the equivalent resistance of three resistors R1, R2 and R3 connected in parallel. Solution
Question 18. Christmas tree lamps are usually connected in series. What will be if one lamp breaks? Solution
Since they are connected in series if one of the lamp is broken, circuit will become incomplete and no electric current will flow . Hence lamp will not glow
Question 19. With the help of a neat diagram derive the expression for the effective resistance when three resistors R1, R2 and R3 are connected is series. Solution
Question 20. Establish a relationship to determine the equivalent resistance R of a combination of three resistors having resistance R1, R2 and R3 connected in series. Calculate the equivalent resistance of the combination of three resistors of 2 Ω, 3 Ω and 6 Ω joined in parallel. Solution
Question 21. State Joule's law of heating. Question 22.
Derive an expression for electric energy consumed in a device in terms of V, I and t, where V is the potential difference applied to it, I is the current drawn by it and t is the time for which the current flows? Question 23.
a. What is meant by electric current? Name and define its SI unit.
b. In a conductor electrons are flowing from B to A. What is the direction of conventional current? Give justification for your answer.
c. A steady current of 1 ampere flows through a conductor. Calculate the number of electrons that flow through any section of the conductor in 1 second. (Charge on electron = $1.6 \times 10^{-19}$ coulomb) Solution
a. This flow of charge in metallic wire due to the potential difference between two conductors used is called electric current. It SI unit is Ampere
1 Ampere = 1 columb /1 sec
b. Conventional current will flow from A to B as it is taken as the flow of positive charge
c. We know 1 ampere meams 1 coulomb per sec. So we need to calculate the number of electrons in 1 coulomb
$n= \frac {1}{1.6 \times 10^{-19}} = 6.25 \times 10^{18} $
Question 24. In electric potential difference a scalar or vector quantity? What do you mean by a potential difference of 1 volt? Solution
electric potential difference is a scalar quantity as it has only magnitude with no direction
The potential difference between two points is said to be one Volt if 1 Joule of work is done in moving 1 Coulomb of electric charge from one point to another.
Question 25.
a. What does an electric circuit mean?
b. Name a device that helps to maintain a potential difference across a conductor in a circuit.
c. When do we say that the potential difference across a conductor is 1 volt?
d.Calculate the amount of work done in shifting a charge of 2 coulombs from a point A to B having potentials 10 V and 5V respectively. Solution
a.Electric circuit is a continuous path consisting of cell (or a battery), a plug key, electrical component(s), and connecting wires in which current flows.
b. Electric cell or battery
c.The potential difference between two points is said to be one Volt if 1 Joule of work is done in moving 1 Coulomb of electric charge from one point to another.
d. Work done = qV where V is Potential difference
V= 10-5= 5 V, q= 2C
Workdone = $2 \times 10 = 10$ J
Question 26. Draw the symbols of commonly used components in electric circuit diagrams for:
(i) An electric cell
(ii) open plug key
(iii) Wires crossing without connection or joining
(iv) Variable resistor
(v) Battery
(vi) Electric bulb
(vii) Resistance
(viii) Wire joint Solution
Question 27. Draw a labeled circuit diagram to study a relationship between the current (I) flowing through a conductor and the potential difference (V) applied across its two ends. State the formula correlating the I in a conductor and the V across it. also show this relationship by drawing a diagram. Question 28. What would be the resistance of a resistor if the current flowing through it is 0.15 A when the potential difference across it is 1.05 V? Solution
R= V/I = 1.05/.15 =7 Ω
Question 29. (a) Name and state the law that gives relationship between the potential difference (V) across the two ends of a conductor and the current (I) flowing through it.
(b) Represent it (Ohm's law) mathematically.
(c) Draw a circuit diagram for the verification of Ohm's law.
(d) Draw the V - I graph for this (Ohm's) law.
Question 30. State and explain Ohm's law. Define resistance and give its SI unit. What is meant by 1 ohm resistance? Draw V - I graph for an ohmic conductor and list its two important features.
Question 31. 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? Solution
Electric resistance of a conductor is the obstruction offered by the conductor to the flow of the current through it. SI unit of resistance is Ohm (O) where 1 Ohm=1 volt/1 Ampere
The resistance of the conductor depends
i.on its length
ii.on its area of cross-section
iii.on the nature of its material
Resistance is given as
$R = \rho \frac {L}{A}$
So if Lenght is doubled ,Resistance is doubled
If radius is doubled , Resistance is one -fourth
Question 32. List two distinguishing features between the resistance and resistivity of a conductor. A wire is stretched so that its length becomes 6/5 times of its original length. If its original resistance is 25 Ω find its new resistance. Give justification for your answer in each case.
Solution
Resistance of a conductor of length L and an area of uniformcross section is
$R =\rho \frac {L}{ A }
Given R = 25Ω
Let us assume that the density of the material remains thesame. Hence the volume of the conductor remains the same.
$A L = A_1 L_1$
$A_1 = \frac {A L }{L_1}
After stretching the wire $L_1 = \frac {6L}{5}$
$A_1 = \frac {5A L }{ 6 L} = \frac {5A}{6}$
