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551.

A certain wire has a resistance R . The resistance of another wire identical with the first except having twice its diameter isA. `2R`B. `0.25R`C. `4R`D. `0.5R`

Answer» Correct Answer - B
552.

A wire of length 5m and radius 1mm has a resistance of 1 ohm . What length of the wire of the same material at the same temperature and of radius 2mm will also have a resistance of 1 ohmA. `1.25m`B. `2.5m`C. `10m`D. `20m`

Answer» Correct Answer - D
553.

In hydrogen atoms, the electron moves in an orbit of radius `5.0xx 10^(-11) m` with a speed of `2.2 xx 10^(6)ms^(-1)`. Find the equivalent curren , Electronic change `= 16 xx 10^(-19)C`

Answer» Correct Answer - `= 1.12 mA`
`I = (e )/(T) = (e )/(2 pi r//v) = (ev)/(2pi r)`
`= ((1.6 xx 10^(-19)) xx 2.2 xx 10^(6))/(2 xx (22//7) xx (5.0 xx 10^(-11))`
`= 1.12 xx 10^(-3)A`
`= 1.12 mA`
554.

What do you understand by sensitiveness of a potentiometer and how can you increase the sensitiveness of a potentiometer?

Answer» The sensitiveness of a potentiometer means the smallest potential difference that can be measured with its help and for a small change in pot. Diff. to be measured it shows a large change in balancing length. The sensitiveness of a potentiometer can be increased by decreasing its potential gradient. This can be achieved,
(a) by increasing the length of potentiometer wire.
(b) If the potentiometer wire is of fixed length, the potential gradient can be decreased by reducing the current in the potentiometer wire circuit by increasing the resistance with the help of rheostat.
555.

Can you interchange the positions of the battery in the auxiliary circuit and cell whose emf is to be determined in potentiometer circuit diagram?

Answer» Correct Answer - cannot
556.

Six cell each of emf `E` and internal resistance `r` are connected in series. If due to over sight, two cells are connected wrongly, then the equivalent emf and internal resistance of the combination isA. `6 E,6 r`B. `4 E,6 r`C. `2 E,6 r`D. `2 E,4 r`

Answer» Correct Answer - c
One wrongly conneted cell in series will cancel out emf of two cells in circuit. Therefore, two wrongly connected cell will cancel out the emf of two cell in series. Hence effective emf of all cells in series `= 6E - 4E = 2E`
Total internal resistance `= r+ r+ ....6 "terms" = 6r`
557.

Five identical lamps , each of resistance `1100 Omega` are connected to `220 V` The reading of an ideal ammeter `A` is A. `(220)/(1100)xx 1A`B. `(220)/(1100)xx 2A`C. `(220)/(1100)xx 3A`D. `(220)/(1100)xx 5A`

Answer» Correct Answer - c
In the given circuit the potential difference across each resistor is `220V` The currect through ammeter in the sum of currect flowing through the three resistance to parallel to the right of ammeter
`:.` Current through ammeter `= 3 xx(220)/(11000)A`
558.

The magnitude and direction of the current in the circuit shown will be A. `(7//3)` A from A to D via FB. `(7//3)` A from D to A via FC. `1.0 A` from A to D via FD. `1.0 A` from D to A via F

Answer» Correct Answer - c
Total resistance of the circuit is
`R = 1+2 xx 3 = 6 Omega`
Effective emf of current `= 10- 4= 6V`
Current `I = ("effectively emf")/("total resistance") = (6)/(6) = 1A`
The direction of current would be from `A` to `D` via `F`
559.

A carbon filament has resistance of `120Omega` at `0^(@)C` what must be te resistance of a copper filament connected in series with resistance at all temperature `(alpha_("carbon")=(-5xx10^(-4))/(``^(@)C),alpha_("copper")=(4xx10^(-3))/(``^(C))`A. `120Omega`B. `15Omega`C. `60Omega`D. `210Omega`

Answer» Correct Answer - B
`R_(1)alpha_(1)=R_(2)alpha_(2)`
560.

A potentiometer having a wire `10 m` long stretched on it is connected to a battery having a steady voltage. A length of potentiometer wire is increase by `100 cm`, find the new position of null point.

Answer» Correct Answer - ` 825 cm`
Let `x` be the emf of battery used in potentiometer wire `= 10 m = 1000 cm `
emf of Lenlache cell `= (epsilon)/(1000) xx 750 V`
New length of potentimeter wire
`= 1000 + 100 = 1100 cm `
Let `l_(1)` be the balancing length of potentiometer wire be the emf of lachacles cell .Then
`(epsilon)/(1000) xx 750 = (epsilon)/(1100) l_(1)`
or `l_(1) = (1100 xx 750)/(1000) = 825 cm`
561.

the ratio of potential gradients is `1:2`, the resistance of two potentiometer wires of same length are `2Omega&4Omega` respectively. The current flowing through them are in the ratioA. `1:2`B. `2:1`C. `1:3`D. `1:1`

Answer» Correct Answer - D
`(i_(1))/(i_(2))=(V_(1))/(V_(2))(R_(2))/(R_(1))`
562.

Four wires of the same diameter are connected, in turn, between two points maintained at a constant potential difference, Their resistivities and lengths are, `rho and L ("wire 1") 1.2rho and 1.2L("wire 2"), 0.9 rho and 0.9L("wire 3") and rho and 1.5L ("wire 4")`. Rank the wires according to hte rates at which energy is dissipated as heat, greatest first,A. `4gt3gt1gt2`B. `4gt2gt1gt3`C. `1gt2gt3gt4`D. `3gt1gt2gt4`

Answer» Correct Answer - 4
Resistance of a wire `R =(pl )/(A)`
Where `p=` respectivity of a wire
l=length of a wire
A=area of a cross-section of a wire
Rate of energy dissipated as heat is `H=(V^(2))/(R)=(V^(2)A)/(pl)`
For a wire `1,H_(1)=(V^(2)A)/(pl)`
For a wire 2,
`H_(2)=(V^(2)A)/( (1,2p)(1.2L))=(0.694 V^(2)A)/(pL)=0.694H_(1)`
For wire 3 .
`H_(3)=(V^(2)A)/((0.9 p)(0.9L))=(1.23V^(2)A)/(plL)=1.23H_(1)`
For a wire 4.
`H_(4)-=(V^(2)A)/((p)(1.4L))=(0.666V^(2)A)/(pL)= 0.666H_(1)`
`therefore H_(3)gt H_(1)gtH_(2)gtH_(4)`.
563.

1 ohm resistance is in series with a Ammeter which is balanced by 75 cm of potentiometer wire. A standard cell of 1.02 V is balanced by 50 cm.t he ammeter shows a reading of 1.5 A. The error in the ammeter reading isA. 0.002 AB. 0.03 A `P_(1)` to `P_(2)`C. 1.01 AD. no error

Answer» Correct Answer - B
`(V_(1))/(V_(2))=(l_(1))/(l_(2))=(75)/(50)impliesV_(1)=1.53V`
`I_(1)=(V_(1))/(I)=1.53A`, error `=1.53-1.50=0.03`
564.

AB is `1` meter long uniform wire of `10 Omega` resistance. Other data are shown in the diagram. Calculate (i) potential gradient along `AB` (ii) length `AO` when galvanometer shown deflection

Answer» Correct Answer - (i)`0.016 V cm^(-1)`(ii)`31.2 cm`
(i) potential gradent along `AB`
`= ((4)/(15v + 10)) (10)/(100) = 0.016 V cm^(-1)`
(ii) current through `0.6 Omega = (1.5)/(1.2 xx 0.6) = (5)/(6) A`
pot diff across `0.3 Omega =(3)/(6) xx 0.6 = 0.5 V`
Across length `AO, V = 0.3 V `is to be balance Let `l` be the length `AO` then
`0.5 = 0.016 xx l or I = (0.5)/(0.016) = 31.2 cm`
565.

1 ohm resistance is in series with a Ammeter which is balanced by 75 cm of potentiometer wire. A standard cell of 1.02 V is balanced by 50 cm.t he ammeter shows a reading of 1.5 A. The error in the ammeter reading isA. 0.002 AB. 0.03 AC. 1.01 AD. no error

Answer» Correct Answer - B
`1.02Vto50cm`
`?to75cm`
`V=(75xx1.02)/(50)=1.53`
error `=1.53-1.5=0.03`
566.

There are n similar conductors each of resistance R . The resultant resistance comes out to be x when connected in parallel. If they are connected in series, the resistance comes out to beA. `(R)/(n)`B. `(R)/(n^(2))`C. `nR`D. `n^(2)R`

Answer» Correct Answer - 4
567.

The total resistance b etween x and y in ohm is:- A. `1Omega`B. `4Omega`C. `(4)/(3)Omega`D. `(2)/(3)Omega`

Answer» Correct Answer - 3
568.

Resistance of a milli ammeter is `R_1` of an ammeter is `R_2` of a voltmeter is `R_3` and of a kilovoltmeter is `R_4`. Find the correct order of `R_1, R_2, R_3` and `R_4`.

Answer» To increase the range of an ammeter a low resistance has to be connected in parallel with galvanometer. Therefore, net resistance decreases,. To increase the range of voltmeter a high resistance has to be connected innseries.So net resistance further increases Therefore the correct order is
`R_4gtR_3gtR_1gtR_2`
569.

A potentiometer having the potential gradient of `2 mV//cm` is used to measure the difference of potential across a resistance of `10 ohm`. If a length of `50 cm` of the potentiometer wire is required to get null point, the current passing through the `10 ohm` resistor is (in `mA`)A. 1B. 2C. 5D. 10

Answer» Correct Answer - D
(d) `V = xl implies iR = xl`
`implies ixx 10 = ((2 xx 10^(-3))/(10^(-2))) xx 50 xx 10^(-2) = 0.1`
`implies i= 10 xx 10^(-3) A = 10 mA`.
570.

Two bulbs when connected in parallel to a source take 60 W each, the power consumed, when they are connected in series with the same source isA. 15 WB. 30 WC. 60 WD. 120 W

Answer» Correct Answer - B
571.

Is electric current a vector or scalar quantity ? Explain

Answer» Electric current is a scaler quantity, because it does not follow the laws of vectors addition, i.e., the angle between the wires carrying the current does not affect the total current in the circuit.
572.

Why do the free electrons in a metal wire, flowing by themselves, not cause any current flow in the wire

Answer» In a metal wire, the free electrons due to thermal motion move at random. There average velocity is zero in one direction. Due to it, there is no current flow in the wire.
573.

Choose the correct alternatives : (a) Alloys of metals usually have (greater/less) resistivity than that of their constituent metals. (b) Alloys usually have much (lower/higher) temperature coefficients of resistance than pure metals. (c ) The resistivity of the alloy manganin in (nearly independent of/ increase rapidly ) with increase of temperature. (d) The resistivity of a typical insulator (e.g. amber) is greater than that of a metal by a factor of the order of `(10^(22) or 10^(3))`.

Answer» (a) greater (b)lower (c ) nearly independent of (d) `10^(22)` .
574.

A high tension (HT) supply of, say 6 Kv must have a very large internal resistance. Why?

Answer» A high tension supply must have a large internal resistance otherwise, if accidently the circuit is shorted, the current drawn will excced safety limit and will cause damage to circuit.
575.

It is easier to start a car engine on a warm day than on a chilly day. Why?

Answer» With increase in temperature (i.e., on a warm day) the internal resistance of a car battery decreases. Due to it, the battery can supply large current which helps in starting the car enegine easily.
576.

What is the order of magnitude of the resistnace of a (dry) human body?

Answer» About `10 k Omega`. This resistance is mainly due to skin through which current enters and leaves our body.
577.

The resistance of a wire is 5 ohm at `50^@C` and 6 ohm at `100^@C`. The resistance of the wire at `0^@C` will beA. `1 ohm`B. `2 ohm`C. `3 ohm`D. `4 ohm`

Answer» Correct Answer - D
(d) `(R_(1))/(R_(2)) = ((1 + alpha t_(1)))/((1 + alpha t_(2))) implies (5)/(6) = ((1 + alpha xx 50))/((1 + alpha xx 100)) implies alpha = (1)/(200) per^(@)C`
578.

A constant current of `4A` passes through a wire for `8s`. Find total charge flowing through that wire in the given time interval.

Answer» Since `i=constant`
`:. /_q=ixx/_ `
`=4xx8`
`=32C`
579.

In a given time of `10s, 40s` electrons pass from right to left. In the same interval of time 40 protons also pass from left to right. Is the average current zero? If not, the find the value of average current.

Answer» No, the average current is not zero. Direction of current is the direction of motin of positive charge or in the opposite of motion of negative charge. So both currents are from left to right and both currents will be added.
`:. I_(av)=I_("electron")+P_("proton")`
`= q_1/t_1+q_2/t_2`
`(40e)/10+(40e)/10`
`= 8e`
`=8xx1.6xx10^-19A`
`=1.28xx10^-18`A
580.

In a conductor, `10^(16)` electrons move from a point A towards point B in 1 milli second. `10^(14)` positive ions move from a point B towards point A in 1 milli second. What is the current in ampere and its direction? Charge on electron = charge on position ion `= 1.6 xx 10^(-19)C`.

Answer» Here, `n_(e)=10^(16) , n_("ion")=10^(14) , t=10^(-3)s`,
Charge on electron or ion, `q=1.6xx10^(-19)C`.
Current, `I=(n_(e) xx q +n_("ion")xxq)/(t)`
`(10^(16)xx1.6xx10^(-19)+10^(14)xx1.6xx 10^(-19))/(10^(-3))`
`=(10^(16)xx1.6xx10^(-19))/(10^(-3)) =1.6A`
The direction of current is from B to A.
581.

The charge flowing in a conductor varies time as, `q=at - 1/2 bt^(2) +1/6 ct^(3)` Where a,b,c are positive constants. Then, find (i) the initial current (ii) the time after which the value of current reaches a maximum value (iii) the maximum or minimum value of current.

Answer» (i) Current, `i=(dq)/(dt)`
`=d/dt(at - 1/2 bt^(2) +1/6 ct^(3))`
`=a-bt +1/2 ct^(2)`
When t =0, initial current , i=a
(ii) For i to be maximum or minimum,
`(di)/(dt)=0= - b +ct` or `t =b/c`
Putting this value of t in (i), we have
`i=a - b xxb/c + 1/2 c xx b^(2)/c^(2) = a - b^(2)/c + b^(2)/(2c) = a - b^(2)/(2c)`
As this value of i is less than that at t=0, it must be minimum. So minimum value of current `a= - (b^(2))/(2c)`
582.

the variation of current I through the cross section of the wire over a time interval of 12 second. Find the charge that flows this wire in 12 seconds.

Answer» Amount of charge flowing through the wire in 12 seconds = area under the `I-t` graph
`=1/2 xx 6xx 6+(12-6)xx6=54C`
583.

shows a plot of current `I` through the cross-section of a wire over a time interval of 10s. Find the amount of charge that flows through the wire during this time period.

Answer» Amount of Charge that flows in 10 seconds is
= area under I - t graph
`= 1/2 xx 5 xx 5 +(10-5) xx 5 = 12.5 + 25= 37.5 C`
584.

The equivalent resistance between points A and B A. `2R`B. `(3)/(4)R`C. `(4)/(3)R`D. `(3)/(5)R`

Answer» Correct Answer - D
585.

In the given network, the euqivalent resistance between A and B is A. `6 Omega`B. `16 Omega`C. `7 Omega`D. `5 Omega`

Answer» Correct Answer - D
586.

Find current through the cell and potential difference between A and D in the circuit shown in the figure

Answer» Correct Answer - `(E)/(R) ; (E)/(2)`
587.

Eight identical 1 volt cells are connected to make a ring as shown in the figure. An ideal voltmeter is connected as shown. What will be its reading ?

Answer» Correct Answer - Zero
588.

A battery of `120 V` and internal resistance `r = 0.5 Omega` is used to charge a `110 V` cell in the circuit shown in the figure. find the range of values of R for which the cell will never get charged.

Answer» Correct Answer - `R lt 5.5 Omega`
589.

In the circuit shown, an ideal cell of emf E is connected in series to a non-ideal ammeter and voltmeter. Reading of the voltmeter is `V_(0)`. When a resistance is added in parallel to the voltmeter its reading becomes `(V_(0))/(10)` and the reading of the ammeter becomes `10` times the earlier value. find `V_(0)` in terms of E.

Answer» Correct Answer - `(10 E)/(11)`
590.

Two rods A and B of same cross-sectional area A and length l are connected in series between a source `(T_(1)=100^(@)C)` and a sink `(T_(2)-0^(@)C)` as shown in figure. The rod is laterally insulated. If `G_(A)` and `G_(B)` are the temperature gradients across the rod A and B, thenA. `(G_(A))/(G_(B))=(3)/(4)`B. `(G_(A))/(G_(B))=(1)/(3)`C. `(G_(A))/(G_(B))=(3)/(4)`D. `(G_(A))/(G_(B))=(4)/(3)`

Answer» Correct Answer - B
591.

Two rods A and B of same cross-sectional area A and length l are connected in series between a source `(T_(1)=100^(@)C)` and a sink `(T_(2)-0^(@)C)` as shown in figure. The rod is laterally insulated. The ratio of the thermal resistance of the rods isA. `(R_(A))/(R_(B))=(1)/(3)`B. `(R_(A))/(R_(B))=3`C. `(R_(A))/(R_(B))=(3)/(4)`D. `(R_(A))/(R_(B))=(4)/(3)`

Answer» Correct Answer - A
592.

Two rods A and B of same cross-sectional area A and length l are connected in series between a source `(T_(1)=100^(@)C)` and a sink `(T_(2)-0^(@)C)` as shown in figure. The rod is laterally insulated. If `T_(A)` and `T_(B)` are the temperature drops across the rod A and B, thenA. `(T_(A))/(T_(B))=(3)/(1)`B. `(T_(A))/(T_(B))=(1)/(3)`C. `(T_(A))/(T_(B))=(3)/(4)`D. `(T_(A))/(T_(B))=(4)/(3)`

Answer» Correct Answer - B
593.

Four moles of an ideal gas is initially in a state A having pressure `2xx10^(5)N//m^(2)` and temperature 200 K . Keeping pressure constant the gas is taken to state B at temperature of 400K. The gas is then taken to a state C in such a way that its temperature increases and volume decreases. Also from B to C, the magnitude of `(dT)/(dV)` increases. The volume of gas at state C is eaual to its volume at state A. Now gas is taken is initial state A keeping volume constant. A total of 1000 J heat is rejected from the sample in the cyclic process. Take `R=8.3J//K//mol`. Which graph between temperture T and volume V for the cyclic process is correct.A. B. C. D.

Answer» Correct Answer - C
594.

Four moles of an ideal gas is initially in a state A having pressure `2xx10^(5)N//m^(2)` and temperature 200 K . Keeping pressure constant the gas is taken to state B at temperature of 400K. The gas is then taken to a state C in such a way that its temperature increases and volume decreases. Also from B to C, the magnitude of `(dT)/(dV)` increases. The volume of gas at state C is eaual to its volume at state A. Now gas is taken is initial state A keeping volume constant. A total of 1000 J heat is rejected from the sample in the cyclic process. Take `R=8.3J//K//mol`. The work done by the gas along path B to C isA. `1000J`B. `-1000J`C. `-7640J`D. `5640 J`

Answer» Correct Answer - C
595.

A voltmeter with resistance `2500 Omega` indicates a voltage of `125 V` in the circuit shown in figure. What is the series resistance to be connected ot voltmeter so that it indicates `100 V`? Consider ideal battery. A. `625 Omega`B. `120 Omega`C. `550 Omega`D. Data are insufficient

Answer» Correct Answer - A
(a) emf should be `125 V`.
for second case: `( 100)/(2500) = (25)/(R ) implies = 625 Omega`
596.

Find the potential difference between the points A and B for the network shown in Fig. 4.52.

Answer» Correct Answer - `0.8 V`
597.

In the circuit shows in Fig. `6.22`, a voltmeter reads `30 V` when it is connected across a `400 omega` resistance. Calculate what the same voltmeter would read when it is connected across the `300 Omega` resistance.

Answer» The voltmeter will show maximum reading if it draw minimum current and maximum current flows through `AB` it is an if the maximum of voltmeter is high .Which is in case i.e.
The voltmeter will is show minimum reading if a draws more current it is so if the resistance of voltmeter is low which in is case c becomes the effective resistance of less then the least resistance connected in parallel
598.

Two moles of a diatomic gas are carried trhough the cycle ABCDA as shown in figure. The segment AB represents an isothermal expansion, the segment BC an adiabatic expansion. The pressure and temperature at A are 5 atm and 600K respectively. The volume at B is twice that at A. The pressure at D is 1 atm. What is the pressure at B?A. `2.5` atmB. 3 atmC. `3.5` atmD. 2 atm

Answer» Correct Answer - A
599.

The resistance of an ideal voltmeter isA. ZeroB. Very lowC. Very largeD. Infinite

Answer» Correct Answer - D
600.

A cell supplies a current `i_(1)` trhough a resistnace `R_(1)` and a current `i_(2)` through a resistance `R_(2)`. The internal resistance of this cell isA. `R_(2)-R_(1)`B. `(i_(1)R_(2)-i_(2)R_(1))/(i_(1)-i_(2))`C. `(i_(2)R_(2)-i_(1)R_(1))/(i_(1)-i_(2))`D. `((i_(1)+i_(2))/(i_(1)-i_(2)))sqrt(R_(1)R_(2))`

Answer» Correct Answer - C