Electric Current in Conductors
Questions for Short Answer
1. Suppose you have three resistors each of value 30 Ω. List all the different resistances you can obtain using them.
Answer: If we need to use all three resistors in combination then we can combine them as
(a) all in series
(b) all in parallel
(c) two in parallel and then third in series
(d) two in series and third parallel to this combination
Diagram for (a) and (b)
(a) All in series:-
As in diagram (a) above, the equivalent resistance is
R =30 Ω +30 Ω +30 Ω =90 Ω.
(b) All in parallel:-
As in diagram (b) above, the equivalent resistance is
1/R =1/30 +1/30 +1/30
→1/R =3/30 =1/10
→R =10 Ω.
(c) Two in parallel, third in series:-
See the diagram (c) below,
Diagram (c) and (d)
Equivalent resistance of two in parallel, r is given as
1/r =1/30 +1/30 =2/30 =1/15
→r = 15 Ω
Now 15 Ω and 30 Ω are connected in series. So the equivalent resistance of the arrangement,
R =15 Ω +30 Ω =45 Ω.
(d) Two in series and third in parallel:-
See the diagram (d) in the diagram. The equivalent resistance of two 30 Ω resistors in series, r =30 Ω +30 Ω =60 Ω.
Now equivalent resistance, R of 60 Ω and 30 Ω in parallel is given as,
1/R =1/60 +1/30 =3/60 =1/20
→R =20 Ω.
If all three are not compulsorily taken together, then we have one resistor of 30 Ω, two resistors in parallel 15 Ω, two resistors in series 60 Ω.
So with these three in hand, we have practically 10 Ω, 15 Ω, 20 Ω, 45 Ω, 60 Ω, and 90 Ω resistances for use.
2. A proton beam is going from east to west. Is there an electric current? If yes, in what direction?
Answer: Yes, protons are positively charged and an electric current is a flow of positive or negative charge. So there is an electric current.
Conventionally, the direction of a current is the direction of positive charge flow. Here it is from east to west.
3. In an electrolyte, the positive ions move from left to right and the negative ions from right to left. Is there a net current? If yes, in what direction?
Answer: Conventionally, the direction of positive charge flow or opposite direction of negative charge flow is the direction of the current. Here, due to both types of ions flow the direction of current is from left to right.
Hence there is a net current, and the direction is from left to right.
4. In a TV tube, the electrons are accelerated from the rear to the front. What is the direction of the current?
Answer: From convention, the direction of electric current is the opposite of the direction of flow of negative charge. Hence, in this case, the direction of the current is from front to rear.
5. The drift speed is defined as vd = Δl/Δt, where Δl is the distance drifted in a long time Δt. Why don't we define the drift speed as the limit of Δl/Δt as Δt →0?
Answer: The path of an electron in the conductor under the influence of an electric field is not a smooth one. It collides with the lattice before drifting a step opposite to the direction of the electric field. Hence, the drift speed is taken as an average speed for a distance Δl in time Δt =Δl/Δt.
It can not be defined as limit Δl/Δt, Δt→0, because it gives the instantaneous speed which will not be equal to the drift speed.
6. One of your friends argues that he has read in previous chapters that there can be no electric field inside a conductor. And hence there can be no current through it. What is the fallacy in this argument?
Answer: In the case of static electricity, the charge given to a conductor resides on its outer surface. But when there is no electrostatic equilibrium, an electric field can be present inside the conductor, and hence there can be electric current through it.
7. When a current is established in a wire, the free electrons drift in the direction opposite to the current. Does the number of free electrons in the wire continuously decrease?
Answer: When a current is established in a wire, it means there is a constant charge Q flowing per second through a cross-section of the wire. The flow of a fixed amount of charge per second means a fixed number of free electrons flows per second opposite to the direction of the current. Since the charge or electron flow rate is fixed in the established current in the conductor, the number of free electrons does not decrease. The required number of electrons is supplied by the negative terminal of the battery.
8. A fan with copper windings in the motor consumes less power as compared to an otherwise similar fan having aluminum windings. Explain.
Answer: For similar fan windings, the copper wire windings will have greater conductance than aluminum wire windings. That means the aluminum wire will have more resistance than the copper wire. For the similar performance of fans, the amount of current should be the same. So heat energy developed per second in the windings i²R will be more in aluminum wires which is a wastage. So the fan having aluminum windings will consume more power.
9. The thermal energy developed in a current-carrying resistor is given by U =i²Rt and also by U = Vit. should we say that U is proportional to i² or to i?
Answer: For a resistor having resistance R, the current i through it can be changed by changing the potential difference V. So in the expression U =Vit, both V and i are variables. Thus it can not be said that U is proportional to i.
While in the expression U =i²Rt, the only i² is variable, R and t being constant. So we should say that U is proportional to i².
10. Consider a circuit containing an ideal battery connected to a resistor. Do "work done by the battery" and "the thermal energy developed" represent two names of the same physical quantity.
Answer: For the ideal battery, the work done by the battery and the thermal energy developed in the resistor is the same physical quantity. For a non-ideal battery, these are different because some energy is dissipated through the internal resistance of the battery.
11. Is work done by a battery always equal to the thermal energy developed in electrical circuits? What happens if a capacitor is connected to the circuit?
Answer: Practically batteries have internal resistances. A part of the work done by the battery comes out as thermal energy developed through this internal resistance. So if there are only resistors in the circuit even then the thermal energy developed in the circuit is not equal to the work done by the battery. Generally, a circuit has many elements in addition to resistors. In that case, work done by the battery is never equal to the thermal energy developed in the circuit. For example, if a capacitor is connected to the circuit, the electrostatic energy stored in the capacitor is ½CV², while the work done by the battery is equal to CV. So the rest ½CV² energy is developed as thermal energy in the circuit.
12. A nonideal battery is connected to a resistor. Is work done by the battery equal to the thermal energy developed in the resistor? Does your answer change if the battery is ideal?
Answer: A part of the work done by the battery is used to develop thermal energy through the internal resistance of the nonideal battery. Only the rest part is developed as thermal energy in the resistor. So the work done by the nonideal battery is not equal to the thermal energy developed in the resistor.
If the battery is ideal, there is no internal resistance in it. So the work done by the battery is equal to the thermal energy developed in the resistor. Here we ignore the negligible resistance of the circuit wiring.
13. Sometimes it is said that "heat is developed" in resistance when there is an electric current in it. Recall that heat is defined as the energy being transferred due to the temperature difference. Is the statement under quote technically correct?
Answer: It is true that the energy transferred due to temperature difference is called heat. But temperature is a state related to the kinetic energy of the molecules of the object. If the kinetic energy of the molecules of the resistance is increased due to the flow of electrons through it (in an electric current electron flow is opposite to the direction of the current) then its temperature increases. The electric potential energy is used to increase the temperature of the resistor. Hence the statement under quote is technically correct.
14. We often say "a current is going through the wire". What goes through the wire, the charge or the current?
Answer: The flow of charge through a conductor is defined as current. So when we say "a current is going through the wire" actually the charge is going through it.
15. Would you prefer a voltmeter or a potentiometer to measure the emf of a battery?
Answer: The potentiometer will be preferred. It so because the potentiometer draws no current from the battery and measures the exact potential difference between the terminals when there is no current flow inside the battery. It gives the correct emf.
In the case of a voltmeter, a small current will flow through it. If the equivalent high resistance of the voltmeter is R and internal resistance of the battery =r, then total resistance in the circuit =R+r. The current in the circuit i = Eₘ/(R+r). The potential difference across the voltmeter = iR which is not exactly equal to the emf Eₘ.
16. Does a conductor become charged when a current is passed through it?
Answer: No. When a current is passed through a conductor, excess electrons are not supplied to it. Only due to the potential difference the number of electrons entering from one end of the conductor is equal to the number of electrons coming out from the other end. So it is not charged.
17. Can the potential difference across a battery be greater than its emf?
Answer: If a battery is used to supply power in a circuit, the potential difference across its terminal cannot be greater than its emf. But the potential difference across it can be kept greater than its emf if another greater emf battery is connected to it just like while charging it.
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Links to the Chapters
Links to the Chapters
CHAPTER- 30- Gauss's Law
CHAPTER- 29- Electric Field and Potential
CHAPTER- 28- Heat Transfer
OBJECTIVE -I
CHAPTER- 26-Laws of Thermodynamics
CHAPTER- 25-CALORIMETRY
Questions for Short Answer
OBJECTIVE-I
OBJECTIVE-II
EXERCISES - Q-11 to Q-18
CHAPTER- 24-Kinetic Theory of Gases
CHAPTER- 23 - Heat and Temperature
CHAPTER- 21 - Speed of Light
CHAPTER- 20 - Dispersion and Spectra
CHAPTER- 19 - Optical Instruments
CHAPTER- 18 - Geometrical Optics
CHAPTER- 17 - Light Waves
CHAPTER- 16 - Sound Waves
CHAPTER- 15 - Wave Motion and Waves on a String
CHAPTER- 14 - Fluid Mechanics
CHAPTER- 13 - Fluid Mechanics
CHAPTER- 12 - Simple Harmonic Motion
CHAPTER- 11 - Gravitation
CHAPTER- 10 - Rotational Mechanics
CHAPTER- 9 - Center of Mass, Linear Momentum, Collision
CHAPTER- 30- Gauss's Law
CHAPTER- 29- Electric Field and Potential
CHAPTER- 28- Heat Transfer
CHAPTER- 26-Laws of Thermodynamics
CHAPTER- 25-CALORIMETRY
Questions for Short Answer
OBJECTIVE-I
OBJECTIVE-II
CHAPTER- 24-Kinetic Theory of Gases
CHAPTER- 23 - Heat and Temperature
CHAPTER- 21 - Speed of Light
CHAPTER- 20 - Dispersion and Spectra
CHAPTER- 19 - Optical Instruments
CHAPTER- 18 - Geometrical Optics
CHAPTER- 17 - Light Waves
CHAPTER- 16 - Sound Waves
CHAPTER- 15 - Wave Motion and Waves on a String
CHAPTER- 14 - Fluid Mechanics
CHAPTER- 13 - Fluid Mechanics
CHAPTER- 12 - Simple Harmonic Motion
CHAPTER- 11 - Gravitation
CHAPTER- 10 - Rotational Mechanics
CHAPTER- 9 - Center of Mass, Linear Momentum, Collision
CHAPTER- 8 - Work and Energy
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CHAPTER- 7 - Circular Motion
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CHAPTER- 6 - Friction
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CHAPTER- 5 - Newton's Laws of Motion
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CHAPTER- 4 - The Forces
The Forces-
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CHAPTER- 3 - Kinematics - Rest and Motion
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CHAPTER- 2 - "Physics and Mathematics"
CHAPTER- 2 - "Physics and Mathematics"
