Team Quanta gladly presents all possible short questions of Electricity & Magnetism – I’s Chapter#04: DC Circuits.
Q.1 Will the drift velocity of electrons in a current carrying metal conductor change when temperature of the conductor is increased?
Answer: Yes, the drift velocity is dependent on the temperature. When temperature is increased, the atom vibrates with higher velocities resulting the collisions between atoms and electrons are increased. So, the velocity with which electrons move inside the conductor (drift velocity) is decreased.
Q.2 What type of temperature coefficient of resistivity is possessed by carbon and copper? Explain your answer
Answer: Like semiconductors, carbon has negative value of temperature coefficient of resistivity, this indicates that the resistivity of carbon decreases with increase in temperature.
And for copper the temperature coefficient of resistivity has positivevalue, means that its resistance increases with increase in temperature.
Q.3 Can a dielectric conduct electricity? Can a conductor have dielectric properties?
Answer: A dielectric material is an insulator material present between the plates of the capacitor. So, dielectric cannot conduct electricity. A conductor cannot have properties like dielectric because it shields electric field.
Q.4 What is the difference between emf and a potential difference?
Answer: Although emf and potential difference are dimensionally same quantities, and often considered equal, but there are some differences between both.
| Potential difference | Emf |
| It is defined as work done per unit charge to move it from one point to another point in an electric field.J/C is the dimension of electric potential. | Emf is the energy provided by its source to unit positive charge to move it across the closed circuit.Emf source provides a non-electrical energy, but as the effect of emf that energy is concerted to electrical energy. |
Q.5 Using the formula of current density $\vec{J}=ne\vec{V_d}$, to find unit of current density in system international.
Answer:
$$J=neV$$
Here n is the charge density of the charge carriers, which has SI unit m-3
e is the charge of electron, its SI unit is
V is the drift velocity of the charge carriers, its SI unit is ms-1
Putting in the above formula:
$$J=m^{-3}.C.ms^{-1}$$
$$J=Cs^{-1}.m^{-2}$$
As $1\ A=1\ C/s$
$$J=Am^{-2}$$
Hence, in system international the unit of current density is $Am^{-2}$
Q.6 Define the time constant.
Answer: Time constant is defined as the time taken by the capacitor to reach maximum current is called time constant. It is equal to the product of the resistance and capacitance.
Q.7 Can we use Kirchhoff’s rules (junction and loop rule) to a circuit containing a capacitor?
Answer: Yes, Kirchhoff’s voltage and current rule can be applied to a circuit containing capacitor. For example, RC circuit.
Q.8 Show that the product of RC has dimensions of time.
Answer:
$$RC=\left(\frac{V}{I}\right)\left(\frac{Q}{V}\right)$$
By ohm’s law
$$V=IR\Rightarrow R=\frac{V}{I}$$
and $C=\frac{Q}{V}$
$$RC=\frac{Q}{I}$$
$$RC=\frac{Q}{\frac{Q}{t}}$$
$$RC=t$$
Q.9 under what circumstances would you want to connect batteries in parallel and in series?
Answer: The batteries are connected parallel when we need potential equal to the potential battery. And the batteries are connected on series when the potential is required to be greater than the potential of individual battery.
Q.10 Define Joule’s law and show that 1 kwh = 3.6 MJ.
Answer:
$$1\ kWh=1000\ W\times3600\ s$$
$$1\ kWh=3.6\times{10}^6\ W.s$$
As $1\ W=1\ Js^{-1}$ and ${10}^6=Mega$
$$1\ kWh=3.6\times{10}^6\ Js^{-1}s$$
$$1kWh=3.6\ MJ$$
Q.11 A capacitor, resistor and battery are connected in series. The charge stored by capacitor is unaffected by the resistance of the resistor. What purpose then is served by the resistor?
Answer: The time constant of RC series circuit is given as $\tau=RC$. If resistor is notconnected in series withcapacitor, the charge grows in capacitor immediately and capacitor may burn. The purpose or presence of resistor in a circuit is to control charging and discharging of capacitor.
Q.12 Does the time required for the charge on a capacitor in RC circuit to build up to a given fraction of its final value depend upon on the value of the applied emf?
Answer: The time constant of RC series circuit is given as $\tau=RC$. The growth of chargein capacitor is given as:
$$q=CV\ (1-e^{-\frac{t}{RC}})$$
It shows that time required for the charge on a capacitor in RC circuit to build up toa given fraction of its final value does not depend upon on the value of the applied emf V but depends upon values of Rand C.
Q.13 What do you mean by a node in dc circuit?
Answer: The point of a circuit where three or more wire segments of circuit elements are joined together is called junction or node.
Q.14 State Kirchhoff’s node rule?
Answer: Kirchhoff s current rule states that algebraic sum of all currents meeting at a node of circuit is zero
$$\Sigma I=0$$
Q.15 Explain why the resistance of a ammeter should be very small as compared to other resistances in the circuit.
Answer: The resistance of the ammeter should be very small as compared to other resistances in the circuit. Otherwise, the very presence of the meter would change. The ammeter is always connected in series with circuit element for measurement of current through that element, so that it cannot draw any potential difference from circuit due to its small resistance.
Q.16 Does the direction of emf provided by the battery depend upon the direction of current flow through a battery?
Answer: Yes, the direction of emf provided by the battery depends upon the direction of current flow through a battery.
Q.17 Devise a method for measuring the emf of a battery and the internal resistance of a battery.
Answer: By using potentiometer, the emf of battery and internal resistance of a battery can be measured.
Q.18 What is the origin of the internal resistance of a battery. Does this depend upon the age or size of the battery?
Answer: The origin of the internal resistance of a battery is electrolyte present between the two electrodes. The opposition to flow of charges due to electrolyte of battery is called its internal resistance. It cannot be separated from battery. The internal resistance depends upon the age or Size of the battery because amount of electrolyte changes with age or size.
Q.19 Explain why the resistance of a voltmeter should be very large as compared to the resistance across which the Pd is to be measured.
Answer: The resistance of a voltmeter be very large as compared to any circuit element across which the voltmeter is connected. Otherwise, significant current would passthrough the meter, changing the current through the circuit element in parallel with the meter and consequently changing the Pd being measured. The voltmeter is always connected in parallel to circuit element for measurement of Pd. So that it cannot drawn any current from the circuit due to its high resistance.
Q.20 What volt is the unit of electromotive force? Define it.
Answer: When a voltage is generated by a battery, or by the magnetic force according to Faraday’s Law, this generated voltage’ has been traditionally called an “electromotive force” or emf. The emf represents energy per unit charge which has been made available by the generating mechanism and is not a “force”. The term emf is retained historical reasons.
It is useful to distinguish voltages which arc generated from the voltage changes which occur in a circuit because of energy dissipation, e.g., in a resistor. The unit of electromotive force is called volt and defined as work per unit charge is equal to volt.
Q.21 It is extremely dangerous to use a plug in a radio of 220volts, near a bath tub when you are taking a bath, why?
Answer: Electric current can pass through water. The plug near the bath tub becomes wet and current can leak into the thin layer of water upon it. This may cause a severe shock to the person opening a plug.
Q.22 If positive and negative connections to terminals of an automobile battery were reversed, would you expect the automobile light to function?
Answer: Yes, light will function because light is produced by heating of filament in automobile light and heating does not depend upon direction of flow of current.
Q.23 Why a thin region of a light bulb filament has more possibility to burn then the thicker one?
Answer: We know the temperature of conductor depends upon resistance. If some current passes through light bulb, the temperature of thin region will be more than that of thick region because resistance of a conductor is inversely proportional to its cross-sectional area i.e. $R\propto1/A$. But area of thick region is greater than that of thin region. So, resistance of thin region will be greater than that of thick’ region. Thus, more heat will be produced in the thin region which will make its temperature higher. Hence this higher temperature has more Possibility to bum thin region than the thicker one.
Q.24 Discuss the difficulties of testing whether the filament of light bulb obeys Ohm’s law?
Answer: As temperature increases, resistance of filament goes on increasing according to the relation;
$$R_T=R_\circ(1+\alpha\Delta T)$$
Where is temperature coefficient and $\Delta T$ is rise in temperature. It means that temperature of a lighted bulb doesn’t remains constant, so its filament does not obey Ohm’s law. Thus, the main difficulty in testing whether the filament of lighted bulb obeys Ohm’s law is the change in its temperature with the flow of current and change in electrical resistance.
Q.25 Under what circumstances can the terminal potential difference of a battery exceed its emf? Under what conditions these two are equal?
Answer: The terminal potential difference is greater than emf of battery when battery connected in circuit is being charged by external charger. The terminal potential difference is equal to emf of battery when battery has no internal resistance or external resistance is infinite.
Q.26 A potential difference is applied across ends of a copper wire. What is the effect on drift velocity of free electrons by:
- Increasing potential difference.
- Decreasing length.
- Decreasing temperature.
Answer: By increasing value of potential difference, the value of electric field increases which causes the increase in drift velocity of electrons. When length of wire is decreased, then the value resistance of wire will also decrease. Thus, the current flowing will increase. It means that drift velocity also increases. When temperature decreases, then resistance of wire decreases, Thus the current will increase due to which drift velocity will also increase.
Q.27 How a galvanometer can be modified into voltmeter and ammeter?
Answer: A galvanometer can be changed into voltmeter by connecting a suitable high resistance in series to galvanometer. A galvanometer can be changed into ammeter by connecting a shunt resistance in parallel to galvanometer.
Q.28 What is effect on measured values of potential differences if we assume that potential of earth is +100V instead of zero?
Answer: If we assume that potential of earth is $100V$ instead of $100V$, there is no effect on measured values of potential difference, however potential will be changed.
Q.30 An atom is normally electrically neutral. Why then should on alpha particle be deflected by the atom under any circumstances?
Answer: An atom is normally electrically neutral; when α particle passes near an atom, it will be deflected because nucleus of atom is positively charged and is like a hard sphere having no free space.
Q.31 How does the relation V=iR apply to resistors that do not obey Ohm’s law?
Answer: The resistors that do not obey usual form of Ohm’s law $V\ =\ iR$, for them Ohm’s law is written in form,
$$i=\beta V^m;\ \ \ \ \ \ \ \ \ \beta\ \ and \ m\ are\ constants.$$
Ohm’s law may also be written in form,
$$\vec{J}=\sigma\vec{E};\ \ \ \sigma\ \ is\ conductivity$$
Q.32 What special characteristics must heating wire have?
Answer: The heating wire must dissipate power at high rate which is possible when wire has small cross-sectional area and high resistance.
Q.33 Why is it better to send 10MW of electric power long distances at 10kV rather than 220V?
Answer: We know that power can be expressed as $P=V^2/R.$. It is clear that when resistance is very large, power losses are the minimum. So, it is better to send 10MW of electric power along distances at 10kV rather than 220V.
Q.34 Five wires of same length and diameter are connected in turn between two points maintained at constant potential difference. Will internal energy be developed at faster rate in wire of largest resistance?
Answer: No, internal energy be developed at faster rate in wire of smallest resistance.
Q.35 The relation R=v/i shows that resistance of a conductor is directly proportional to potential difference. What do you think of this proportionality?
Answer: The relation $R\propto V$ is not physically acceptable because i is not constant in above mentioned equation. However, $V\propto i$ is correct provided R is constant.
Q.36 Device a method for measuring emf and the internal resistance of a battery.
Answer: The emf and the internal resistance of a battery can be measured by using potentiometer.
Q.37 Under what circumstances would you want to connected resistors in parallel and in series?
Answer: To increase equivalent resistance, resistances are connected in series and to decrease equivalent resistance, resistances are connected in parallel.
Q.38 Use formula for current density $\vec{J}=ne{\vec{v}}_d$ to find unit of current density in SI system.
Answer: From given relation, unit of current density J is,
$$\frac{C\times m/s}{m^3}=\frac{A}{m^2}$$
Q.39 Why is it not possible to measure the drift speed for electron for timing of their travel along a conductor?
Answer: The drift speed of electrons travelling along a conductor is very small and equation $v_d=s/t$ shows that it is impossible to measure drift speed by measuring time to such small dimensions.
Q.40 What is the origin of the internal resistance of a battery? Does this depend on the age or size of the battery?
Answer: Every real battery has internal resistance which is due to electrolyte between two electrodes. The opposition to flow of charges due to electrolyte of battery is called its internal resistance. It depends upon age and size of the battery.
Q.41 Often, you might have noticed birds sitting safely on high tension wires. Why are they not electrocuted even when sitting on a part of wire where insulation has worn off?
Answer: When a bird is sitting on a high tension wire without insulation, the potential difference between its two feet is zero as both feet are on same potential $\Delta V=0$
$$i=\frac{\Delta V}{R}=\frac{0}{R}=0$$
Hence no current flows through body of the bird and it is not electrocuted.
Q.42 Name other physical quantities that like current are scalars having a sense represented by an arrow in a diagram?
Answer: There are many physical quantities like current which are scalars having a sense represented by an arrow in a diagram. One of them is emf.
Q.43 Why the resistance of metallic conductor increases with rise in its temperature?
Answer: When temperature of conductor increases, atoms of conductor begin to vibrate with larger amplitude and disturb the motion of free electrons resulting, an increase in resistance of that conductor.
Q.44 The current in an electric bulb rises to a maximum value almost at instant the bulb is turned on. The current then decreases significantly, why does current decreases?
Answer: Before the bulb is turned on, its filament is at room temperature resistance is low. When it is turned on, the current rises to maximum. Due to passage of current, heat is dissipated and temperature of filament rises and resistance. From $i=V/R$ when resistance increases then current decreases.
Q.45 What is the difference between emf and terminal potential difference?
Answer: When battery is not supplying current then voltage across it is called emf. When battery is supplying current to external circuit then voltage across its terminals is called terminal potential difference.
Q.46 Kirchhoff’s rules are related to certain conservation laws. Name these laws.
Answer: Kirchhoff’s 1st rule i.e. junction rule is based on conservation of charge and 2nd rule called loop rule is based on conservation of energy.
Q.47 Describe briefly some possible designs of variable resistors.
Answer: There are various designs of variable resistors. One of them is rheostat.
Q.48 A capacitor resistor and battery are connected in series. The charge that the capacitor stores is unaffected by the resistance of the resistor. What purpose then is served by the resistor?
Answer: The purpose of presence of resistance in the above mentioned circuit is to control charging and discharging of capacitor.
Q.49 Does time required for charge on capacitor in RC circuit to build up to a given fraction of its final value depend upon value of applied emf?
Answer: Growth of charge in capacitive circuit is governed by relation,
$$q=C\varepsilon\left(1-e^{-\frac{t}{RC}}\right)$$
Here $t_c=RC$ is time constant of circuit and it depends on R & C and not on emf e.
Q.50 What is charge on a wire when a current flows through wire?
Answer: The net charge on wire is zero even though there is drifting of free electrons, the total number of electrons and protons in wire are equal.
Q.51 (a)-Why should an ammeter be always connected in series in circuit? (b)- Why should an ammeter have a very low resistance?
Answer: (a)- An ammeter should be always connected in series in circuit so that same current should flow through it as is flowing in given circuit.
(b)-When an ammeter is connected in series with circuit, the current to be measured is upset by the insertion of ammeter. In order to minimize this error, resistance of ammeter should be very small as compared with total resistance of circuit.
Q.52 When charge carriers reach the terminals of battery, what happens to their velocity?
Answer: Their motion is accelerated and velocity increases.
