A cell, a resistor, a key and ammeter are arranged as shown in the circuit diagrams of Figure 12.1. The current recorded in the ammeter will be
maximum in (i)
maximum in (ii)
maximum in (iii)
the same in all the cases
In the following circuits (Figure 12.2), heat produced in the resistor or combination of resistors connected to a 12 V battery will be
same in all the cases
minimum in case (i)
maximum in case (ii)
maximum in case (iii)
Electrical resistivity of a given metallic wire depends upon
its length
its thickness
its shape
nature of the material
A current of 1 A is drawn by a filament of an electric bulb. Number of electrons passing through a cross section of the filament in 16 seconds would be roughly
1020
1016
1018
1023
Identify the circuit (Figure 12.3) in which the electrical components have been properly connected.
(i)
(ii)
(iii)
(iv)
What is the maximum resistance which can be made using five resistors each of 1/5 Ω?
1/5 Ω
10 Ω
5 Ω
1 Ω
What is the minimum resistance which can be made using five resistors each of 1/5 Ω?
1/5 Ω
1/25 Ω
1/10 Ω
25 Ω
The proper representation of series combination of cells (Figure 12.4) obtaining maximum potential is
(i)
(ii)
(iii)
(iv)
Which of the following represents voltage?
Work done / (Current × Time)
Work done × Charge
(Work done × Time) / Current
Work done × Charge × Time
A cylindrical conductor of length \(l\) and uniform area of cross-section \(A\) has resistance \(R\). Another conductor of length \(2l\) and resistance \(R\) of the same material has area of cross section
A/2
3A/2
2A
3A
A student carries out an experiment and plots the V–I graph of three samples of nichrome wire with resistances \(R_1, R_2\) and \(R_3\) respectively (Figure 12.5). Which of the following is true?
\(R_1 = R_2 = R_3\)
\(R_1 > R_2 > R_3\)
\(R_3 > R_2 > R_1\)
\(R_2 > R_3 > R_1\)
If the current \(I\) through a resistor is increased by 100% (assume that temperature remains unchanged), the increase in power dissipated will be
100 %
200 %
300 %
400 %
The resistivity does not change if
the material is changed
the temperature is changed
the shape of the resistor is changed
both material and temperature are changed
In an electrical circuit three incandescent bulbs A, B and C of rating 40 W, 60 W and 100 W respectively are connected in parallel to an electric source. Which of the following is likely to happen regarding their brightness?
Brightness of all the bulbs will be the same
Brightness of bulb A will be the maximum
Brightness of bulb B will be more than that of A
Brightness of bulb C will be less than that of B
In an electrical circuit two resistors of 2 Ω and 4 Ω respectively are connected in series to a 6 V battery. The heat dissipated by the 4 Ω resistor in 5 s will be
5 J
10 J
20 J
30 J
An electric kettle consumes 1 kW of electric power when operated at 220 V. A fuse wire of what rating must be used for it?
1 A
2 A
4 A
5 A
Two resistors of resistance 2 Ω and 4 Ω when connected to a battery will have
same current flowing through them when connected in parallel
same current flowing through them when connected in series
same potential difference across them when connected in series
different potential difference across them when connected in parallel
Unit of electric power may also be expressed as
volt ampere
kilowatt hour
watt second
joule second
A child has drawn the electric circuit to study Ohm’s law as shown in Figure 12.6. His teacher told that the circuit diagram needs correction. Study the circuit diagram and redraw it after making all corrections.
[Figure]
[Figure]
Three 2 Ω resistors, A, B and C, are connected as shown in Figure 12.7. Each of them dissipates energy and can withstand a maximum power of 18 W without melting. Find the maximum current that can flow through the three resistors.
[Figure]
Maximum current through resistor A is \( \sqrt{\dfrac{18}{2}} = 3 \text{ A} \).
Thus the maximum current through resistors B and C each is \( 3 \times \dfrac{1}{2} = 1.5 \text{ A} \).
Should the resistance of an ammeter be low or high? Give reason.
The resistance of an ammeter should be as low as possible. Ideally, it should be zero ohm so that it does not affect the current in the circuit.
Draw a circuit diagram of an electric circuit containing a cell, a key, an ammeter, a resistor of 2 Ω in series with a combination of two resistors (4 Ω each) in parallel and a voltmeter across the parallel combination. Will the potential difference across the 2 Ω resistor be the same as that across the parallel combination of 4 Ω resistors? Give reason.
[Figure]
[Figure]
Yes. The total resistance of the parallel combination is 2 Ω, so the potential difference across the 2 Ω resistor is the same as that across the parallel combination.
How does use of a fuse wire protect electrical appliances?
If a current larger than a specified value flows through a circuit, the temperature of the fuse wire increases to its melting point. The fuse melts and the circuit breaks, protecting the appliances.
What is electrical resistivity? In a series electrical circuit comprising a resistor made up of metallic wire, the ammeter reads 5 A. The reading of the ammeter decreases to half when the length of the wire is doubled. Why?
Electrical resistivity \( \rho \) is the resistance of a wire of unit length and unit cross-section. When the length of the wire is doubled, resistance becomes \( R = \rho \dfrac{l}{A} \) and thus doubles. Since \( V = RI \) remains unchanged, current becomes half.
Three incandescent bulbs of 100 W each are connected in series in an electric circuit. In another circuit another set of three bulbs of the same wattage are connected in parallel to the same source.
(a) Will the bulbs in the two circuits glow with the same brightness? Justify your answer.
(b) Now let one bulb in both the circuits get fused. Will the rest of the bulbs continue to glow in each circuit? Give reason.
(a) Comparison of brightness in series and parallel:
In the series combination, the total resistance is three times that of one bulb. Hence the current in the series circuit is one-third of the current in the parallel circuit. Since power is proportional to \( I^2 R \), each bulb in the parallel combination receives higher current and therefore glows more brightly. Thus, the bulbs in the two circuits do not glow with the same brightness; the bulbs in parallel glow more brightly.
(b) Effect of one bulb getting fused:
In the series circuit, when one bulb gets fused, the circuit becomes open, current becomes zero, and none of the bulbs glow.
In the parallel circuit, each bulb has an independent path. When one bulb gets fused, the remaining bulbs continue to glow with the same brightness because their individual circuits remain complete.
State Ohm’s law. How can it be verified experimentally? Does it hold good under all conditions? Comment.
Statement of Ohm’s Law: Ohm’s law states that the potential difference \( V \) across a conductor is directly proportional to the current \( I \) flowing through it, provided physical conditions such as temperature remain constant. Thus, \( V \propto I \), or \( V = IR \).
Experimental Verification:
Validity of Ohm’s Law: Ohm’s law does not hold under all conditions. It fails when temperature changes significantly, in semiconductors, in filament lamps where resistance changes with heat, and in electrolytes where current flow is ionic. It applies only to ohmic conductors at constant temperature.
What is electrical resistivity of a material? What is its unit? Describe an experiment to study the factors on which the resistance of conducting wire depends.
Electrical Resistivity: Electrical resistivity \( \rho \) of a material is defined as the resistance of a conductor of unit length and unit cross-sectional area. It is a measure of how strongly a material opposes the flow of electric current.
Unit: The SI unit of resistivity is ohm-metre (\( \Omega m \)).
Experiment to Study Factors Affecting Resistance:
The resistance \( R \) of a conductor depends on:
Using a circuit with a cell, ammeter, voltmeter, key and wires of different lengths, thickness and materials, readings of \( V \) and \( I \) are taken for each configuration. The resistance is calculated using \( R = V/I \). It is observed that resistance increases with length, decreases with increase in thickness, and varies for different materials even with identical dimensions.
How will you infer with the help of an experiment that the same current flows through every part of the circuit containing three resistances in series connected to a battery?
Verification of equal current in a series circuit:
This confirms that the same current flows through every component in a series circuit because there is only one path for current flow.
How will you conclude that the same potential difference (voltage) exists across three resistors connected in a parallel arrangement to a battery?
Verification of equal potential difference in a parallel circuit:
This shows that in a parallel circuit, each resistor gets the same potential difference because all are connected directly across the same two points of the battery.
What is Joule’s heating effect? How can it be demonstrated experimentally? List its four applications in daily life.
Joule’s Heating Effect: When an electric current \( I \) flows through a resistor \( R \) for time \( t \), the heat produced is given by \( H = I^2 R t \). This phenomenon is known as the Joule’s heating effect.
Demonstration: A circuit is set up with a battery, key, ammeter, and a coil immersed in water. When current flows through the coil, the temperature of water rises, demonstrating heat production due to current.
Applications:
Find the following in the electric circuit given:
(a) Effective resistance of two 8 Ω resistors in the combination
(b) Current flowing through 4 Ω resistor
(c) Potential difference across 4 Ω resistance
(d) Power dissipated in 4 Ω resistor
(e) Difference in ammeter readings, if any
(a) Effective resistance: The two 8 Ω resistors are in parallel. Their effective resistance is \( R = \dfrac{R_1 R_2}{R_1 + R_2} = \dfrac{8 \times 8}{8 + 8} = 4\, \Omega \).
(b) Current through 4 Ω resistor: Total resistance in the circuit is \( 4 + 4 = 8\, \Omega \). Current \( I = \dfrac{V}{R} = \dfrac{8}{8} = 1\, \text{A} \).
(c) Potential difference across 4 Ω resistor: \( V = IR = 1 \times 4 = 4 \text{ V} \).
(d) Power dissipated: \( P = I^2 R = 1^2 \times 4 = 4 \text{ W} \).
(e) Difference in ammeter readings: There is no difference because the same current flows through all elements of a series circuit.