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951.

Whether electric field inside potentiometer wire is constant or variable ?

Answer» Electric field intensity `E= V//l = a` constant.
952.

Why do we prefer a potentiometer to measure emf of a cell rather than a voltmeter ?

Answer» At null point, a potentiometer does not draw any current from the cell whose emf is to be determined, whereas a voltmeter, always draws some little current. Therefore, emf measured by voltmeter is slightly less than actual value of emf of the cell.
953.

Two adiabatic containers have volumes `V_(1)` and `V_(2)` respectively. The first container has monoatomic gas at pressure `p_(1)` and temperature `T_(1)`. The second container has another monoatomic gas at pressure `p_(2)` and temperature `T_(2)`. When the two containers are connected by a narrow tube, the final temperature and pressure of the gases in the containers are P and T respectively. ThenA. `T=(p_(1)V_(1)T_(2)+p_(2)V_(2)T_(1))/(p_(1)V_(1)+p_(2)V_(2))`B. `T=(p_(1)V_(1)T_(2)+p_(2)V_(2)T_(1))/(p_(1)V_(2)+p_(2)V_(1))`C. `p=(p_(1)V_(2)+p_(2)V_(1))/(V_(1)+V_(2))`D. `p=(p_(1)V_(1)+p_(2)V_(2))/(V_(1)+V_(2))`

Answer» Correct Answer - D
954.

A circuit is arranged as shown. Then, the current from `A` to `B` is A. `+ 500 mA`B. `+ 1.5 mA`C. `- 250 mA`D. `- 500 mA`

Answer» Correct Answer - A
(a) `I = (sum (E // r))/(1 + R sum (1//r))`
`= ((5)/(15) + (10)/(10))/(1 + 10 [ (1)/(15) + (1)/(10)]) = (1)/(2) A = 500 mA`
955.

In the circuit of adjoining figure the current through `12 Omega` resister will be A. `1 A`B. `(1)/(5) A`C. `(2)/(5) A`D. `0 A`

Answer» Correct Answer - D
(d) Let the current in `12 Omega` resistance is `i`
Applying loop theorem in closed mesh `AEFCA`
`12i = - E + E = 0 :. i= 0`
956.

In the circuit of adjoining figure the current through `12 Omega` resister will be A. `1A`B. `(1)/(5)A`C. `(2)/(5)A`D. 0A

Answer» Correct Answer - D
957.

A battery of emf `2.0 V` and internal resistance `0.10 Omega` is being charged with a current of `5.0 A`. Find the potential difference between the terminals of the battery?

Answer» Potential drop across internal resistance `=Ir=0.1xx5=0.5V`
Hence potential difference across terminals `=E+Ir=2+0.5=2.5` volt.
958.

The reading of the ideal voltmeter in the adjoining diagram will be A. 4VB. 8VC. 12VD. 14V

Answer» Correct Answer - B
959.

A current of 7 A flows through the circuit as shown in the figure the potential difference across points B and D isA. `5V`B. `3V`C. `10V`D. `7V`

Answer» Correct Answer - A
`i_(1)=(ixxR_(2))/(R_(1)+R_(2))`
`i_(2)=(ixxR_(1))/(R_(1)+R_(2))`
960.

An ammeter A is connected as shown in the diagram. Ammeter reading isA. `(E)/(r)`B. `(2E)/(r)`C. `(r)/(2E)`D. `(E)/(2r)`

Answer» Correct Answer - B
`i=(5E)/(r)-(3E)/(r)=` ….
961.

If a rod has resistance `4 Omega` and if rod is turned as half cycle then the resistance along diameterA. `1.56 Omega`B. `2.44 Omega`C. `4 Omega`D. `2 Omega`

Answer» Correct Answer - C
962.

The equivalent resistance across XY in fig.A. `r`B. `2r`C. `4r`D. `(r)/(2)`

Answer» Correct Answer - D
combination of resistors
963.

The equivalent resistance across A and B isA. `2Omega`B. `4Omega`C. `8Omega`D. `12Omega`

Answer» Correct Answer - B
combination of resistors
964.

If the resistance of a circuit having 12 V source is increased by `4Omega` the current drops by 0.5 A. What is the original resistance of circuitA. `4Omega`B. `8Omega`C. `16Omega`D. `(1)/(16)Omega`

Answer» Correct Answer - B
`V=iR`
`12=(i-0.5)(R+4)`
965.

When `n` wires which are identical are connected in series, the effective resistance exceeds that when they are in parallel by `(X)/(Y)Omega`. Then the resistance of each wire isA. `(xn)/(y(n^(2)-1))`B. `(yn)/(x(n^(2)-1))`C. `(xn)/(y(n-1))`D. `(yn)/(x(n-1))`

Answer» Correct Answer - A
`R_(S)=R_(p)+((X)/(Y))`
966.

An electric current is passed through a circuit containing two wires of the same material connected in parallel. If the lengths and radii of the wire are in the ratio `(4)/(3)` and `(2)/(3)`, then the ratio of the currents passing through the wires will beA. `(1)/(3)`B. `(3)/(1)`C. `(4)/(3)`D. `(3)/(4)`

Answer» Correct Answer - A
`V-iR` `V=` constant
`i_(1)R_(1)=i_(2)R_(2)`
`(i_(1))/(i_(2))=(R_(2))/(R_(1))`
`thereforeRprop(l)/(A)`
967.

An electric current is passed through a circuit containing two wires of the same material connected in parallel. If the lengths and radii of the wire are in the ratio `(4)/(3)` and `(2)/(3)`, then the ratio of the currents passing through the wires will beA. 3B. `1//3`C. `8//9`D. 2

Answer» Correct Answer - B
968.

A student records `Delta Q, Delta U` and `Delta W` for a thermodynamic cycle `A rarr B rarr C rarrA`. Certain entries are missing. Find correct entry in following options. A. `W_(BC)=-70J`B. `Delta Q_(CA)=130J`C. `Delta U_(AB)=190 J`D. `Delta U_(CA)=-160J`

Answer» Correct Answer - D
969.

In parallel combination of n cells, we obtainA. more voltageB. more currentC. less voltageD. less current

Answer» Correct Answer - B
In parallel combination of cells the voltage across the terminals is same and resistance is minimum. Therefore from V=IR. The current drawn from cell combination will be more.
970.

If n cells each of emf E and internal resistance rare connected in parallel, then the total emf and internal resistances will beA. `epsi, (r)/(n)`B. `epsi,nr`C. `"n"epsi,(r)/(n)`D. `"n"epsi,nr`

Answer» Correct Answer - A
In the parallel combination, `(epsi_("eq"))/(r_("eq"))=(epsi_(1))/(r_(1))+(epsi_(2))/(r_(2))+,.....+(epsi_(n))/(r_(n))`
`(1)/(r_("eq"))=(1)/(r_(1))+(1)/(r_(2))+...+(1)/(r_n)`
`(therefore epsi_(1)=epsi_(2)=epsi_(3)=.....=epsi_(n)=epsi and r_(1)=r_(2)=r_(3)=r...r_(n)=r)`
`therefore (epsi_("eq"))/(r_("eq))=(epsi)/(r)+(epsi)/(r)+......+(epsi)/(r)=n(epsi)/(r)..(i)`
`(1)/(r_("eq"))=(1)/(r)+(1)/(r)+....+(1)/(r)=(n)/(r)`
`r_("eq")=r//n...(ii)`
From (i) and (ii)
`e_("eq")=n(epsi)/(r)xxr_("eq")=nxx(epsi)/(r)xx(epsi)/(n)=epsi`
971.

A potential difference of 120 V is applied to a coil at temperature of `12^@C` and the current is 6A. What will be the mean temperature of the coil when the curreny has fallen to 3 A, the applied voltage being the same as before ? Given temperature coefficient of resistance coil is `.00427^@C^(-1)` at `0^@C`.

Answer» In second case the current decreases due to incerese in resistance on heating. Here
`R_(12)=V/I=120/6=20 Omega`
If `t^@C` is the temperature at which current falls
to 3A, then `= R_(1)=120/3=40 Omega`
As `R_(t)=R_(0)(1+alpha t)`
So `R_(12)=R_(0)(1+alpha xx12)`
or `20 =R_(0)(1+.00427 xx 12)`
and `R_(t) = R_(0)(1+alpha t)or 40=R_(0)(1+.00427 t)`
`:. 40/20 =(1+0.00427 t)/(1+0.00727 xx12)`
On solving, `t=258^@C`.
972.

If 2 mol of an ideal monatomic gas at temperature `T_(0)` are mixed with 4 mol of another ideal monatoic gas at temperature `2 T_(0)` then the temperature of the mixture isA. `(5)/(3)T_(0)`B. `(3)/(2)T_(0)`C. `(4)/(3)T_(0)`D. `(5)/(4)T_(0)`

Answer» Correct Answer - A
973.

The resistance of a silver wire at `0^(@)C " is " 1.25 Omega`. Upto what temperature it must be heated so that its resistance is doubled ? The temperature coefficient of resistance of silver is `0.00375^(@)C^(-1)`. Will the temperature be same for all silver conductors of all shapes ?

Answer» Correct Answer - `267^(@)`, Yes
974.

A few straings cells in series are to be charge from a `30V` d.c. supply The end of each cutt is `1.35V` and internal resistance is `0.1 Omega` The charging current is `3.0A` in this arrangement how many calls can be charge and what extra resistance is required be the connected in the circuit ?

Answer» Let `n` be the maximum number of cells in series which can be change and `R` is the extra resistance required if `f` is the currentin the circuit then `(nr + R) 1 = 30 - n epsilon`
Hence `epsilon = 1.35 V, r= 0.1 Omega and t = 3.0A`
Thus `(n xx 0.1 + R) xx 3= 30 - n xx 1.35 n (1.35 + 0.3) + 3R =m 30 or 1.65 n + 3R = 50`...(i)
or `n + (3)/(1.65) R = (30)/(1.65) = 18 + (30)/(165) :. n = 3n and (3R)/(1.65) = (30)/(165) or R = 0.1 Omega`
975.

A standard coil marked `3 Omega` is found to have a true resistance of `3.115 Omega` at 300 K. Calculate the temperature at which marking is correct. Temperature coefficient of resistance of the material of the coil is `4.2xx10^(-3) .^(@)C^(-1)`.

Answer» Correct Answer - `290.2 K`
976.

Four wires made of same material have different lengths and radii, the wire having more resistance in the following case isA. `l=100cm, r=1mm`B. `l=50cm, r=2mm`C. `l=100cm, r=(1)/(2)mm`D. `l=50cm, r=(1)/(2)mm`

Answer» Correct Answer - C
`Ralpha(l)/(r^(2))`. Chech the options
977.

Determine the potentials of point A and B with respect to earth

Answer» Current in circute `I = (6)/(1 + 2+ 3) = I A`
potential different across `2 Omega = 1 xx 2 = 2V`
potential different across `3 Omega = 1 xx 3 = 3V`
As earth is at zero potential , so
`V_(A) = V_(C) = 2V` or `V_(A) - 0 = 2V` or `V_(A) = 2V`
and `V_(C) - V_(B) = 3V` or `0 - V_(B) = 3V` or `V_(B) =- 3V`
978.

A wire has a resistance of `6 Omega`. It is cut into two parts and both half values are connected in parallel. The new resistance is ....A. `12 Omega`B. `1.5 Omega`C. `3 Omega`D. `6 Omega`

Answer» Correct Answer - C
979.

Six equal resistances are connected between points P, Q and R as shown in the figure. Then the net resistance will be maximum betweenA. P and QB. Q and RC. P and RD. Any two points

Answer» Correct Answer - A
980.

The three resistances of equal value are arranged in the different combinations shown below. Arrange them in increasing order of power dissipationA. `IIltIltIII`B. `IgtIIIgtII`C. `IltIIIltII`D. `IltIIltIII`

Answer» Correct Answer - A
`P=i^(2)R` Current is same `P=R`
In the first case it is `3r` in second case it is `(2)/(3)r` in third case it is `(r)/(3)` and in fourth case the net resistance is
`(3r)/(2)`
`R_(III)ltR_(II)ltR_(IV)ltR_(I)becauseP_(III)ltP_(II)ltP_(IV)ltP_(I)`
981.

Six equal resistances are connected between points P, Q and R as shown in the figure. Then the net resistance will be maximum betweenA. P and QB. Q and RC. P and RD. any two points

Answer» Correct Answer - A
`R_(PO)=(5)/(11)r,R_(QR)=(4)/(11)r` and `R_(PR)=(3)/(11)r`
`thereforeR_(PQ)` is maximum
Therefore the correct option is (a)
982.

Calculate the radius of the wire of conductance `10 Omega^(-1)` and length `10 cm` whose electrical conductivity is `10^(3) Sm^(-1)`

Answer» Correct Answer - `1.78 mm`
Here,`G = 10 Omega^(-1), 1 = 10 cm = 0.10 m`
`sigma= 10^(3) Omega m^(-1)`
`sigma = (1)/(rho) = (l)/(pir^(2)R) = (lG)/(pir^(2)) or r = sqrt((lG)/(pi sigma))`
`:. r = sqrt((0.10 xx 10)/(314 xx 10^(3))) = 1.78 xx 10^(-2)m = 0.0178 "m"`
983.

Calculate the potential difference between points B and D of the network of resistance shown in figure

Answer» Here, potential differences across ABC = potential differences across ADC = 12 V
Current in arm ABC,
`I_(1)=12/6+4 =1.2A`
pot. Diff. between A and B,
`V_(A) - V_(B)=I_(1) xx 6 =1.2 xx 6=7.2 V`
Current in arm ADC,
`I_(2)=12/8+12=0.6A`
pot. diff. across A and D,
`V_(A) - V_(D) = I_(2) xx 8 = 0.6 xx 8 =4.8 V`
`:. (V_(A) - V_(B)) - (V_(A) - V_(D))= 7.2 - 4.8 = 2.4 V`
or `V_(D) - V_(B) = 2.4 V`
`:. V_(B) - V_(A)= -2.4 V`
It shows that the point D is at higher potential than that of point B.
984.

Six equal resistances each of 4 ohm are connected to form a net work as shown in figure . What is the resistance between A and B ?

Answer» The upper five resistances between A and B will form a balanced wheatstone bridge. Hence there will be no current in arm CO. The equivalent circuit will be as shown in figure. Here, resistance of arm ACB, AOB and Ab are all in parallel. The effective resistance R is given by
`1/R =(1)/((4+4)) + 1/(4+4) + 1/4 = (1+1+2)/8 = 4/8 = 1/2`
`R = 2 Omega`
985.

Resistance of tungsten wire at `150^(@)C` is `133 Omega`. Its resistance temperature coefficient is `0.0045//^(@)C`. The resistance of this wire at `500^(@)C` will beA. `180 Omega`B. `225 Omega`C. `258 Omega`D. `317 Omega`

Answer» Correct Answer - C
(c ) `(R_(150))/(R_(500)) = ([1 + alpha (150)])/([1 + alpha (500)])`. Putting `R_(150) = 133 Omega` and
`alpha = 0.0045//^(@)C`, we get `R_(500) = 250 Omega`
986.

In the circuit shown in figure Find the potential differnece across capacitor.

Answer» When capacitor is fully charged, it fraws no currnet, and hence provides infinite resistance, then no current flows in arm EF. The potential difference across C and F. The resistance of arm AD and they together are in series with resistance of arm DF. The effective resistance between A and F of circuit is,
`R = (3xx6/3+6) + 3 = 2 +3 =5 Omega`
Main in the circuit, `i = 15/5=3 A`
Current through arm BCD
` = 1 xx 3/6+3 = 3xx3/9 = 1 A`
Potential difference across C and D `= 1 xx 3 = 3V`
Current through arm DF, i =3A
Potential differences across D and F `= 3 xx 3 = 9 V`
So, potential difference across C and F `= 3+ 9=12 V`
Thus, potential difference across the capacitor is 12 V
987.

Resistance of tungsten wire at `150^(@)C` is `133 Omega`. Its resistance temperature coefficient is `0.0045//^(@)C`. The resistance of this wire at `500^(@)C` will be

Answer» Correct Answer - `215 Omega`
Here, `R_(160) = 132 Omega R_(400) = ?`
`alpha = 4.5 xx 10^(-3).^(@)C^(-1)`
Now `R_(t) = R_(0)(1 + alpha t)`
`:. R_(160) = R_(0) [1 + (4.5 xx 10^(-3))xx 100]`
or `132 = R_(0)[1+4.5 xx 10^(-3)xx 100]`……(i)
and `R_(400) = R_(0) [1 + 4.5 xx 10^(-3)xx400]`.....(ii)
Dividing (ii) by (i) we get
`(R_(400))/(132) = (1+ 4.5 xx 10^(-3) xx 400)/(1+ 4.5 xx 10^(-3) xx 400)`
`= (1+ 1.80)/(1+ 0.72) = (2.80)/(1.72) = 1.63`
`R_(400) = 132 xx 1.63 = 215 Omega`
988.

Four conductors of same resistance connected to form a square. If the resistance between diagonally opposite corners is 8 ohm, the resistance between any two adjacent corners isA. 32 ohmB. 8 ohmC. `(1)/(6)` ohmD. 6 ohm

Answer» Correct Answer - D
combination of resistors
989.

The electrical resistance of a mercury column in a cylindrical container is `R` the mercury is poured into another cylindrical container with half the radius of cross-section. The resistance of the mercury column isA. `R`B. `2R`C. `16R`D. `5R`

Answer» Correct Answer - C
`R=(rhol)/(A),V=Al`
990.

The temperature coefficient of resistance of a wire is 0.00125 per `.^oC`. At 300K, its resistance is 1 `Omega`. The resistance of the wire will be 2 `Omega` atA. 1154 KB. 1100 KC. 1400 KD. 1127 K

Answer» Correct Answer - B
`R_theta = R_(theta_0) [1 +alpha(theta - theta_0)]`
`2 = 1[1 + 0.00125 (theta - 300)]`
`theta = (1)/(0.00125) + 300 = 1100 K`.
991.

The specific resistance of all metals is most affected byA. TemperatureB. PressureC. Degree of illuminationD. Applied magnetic field

Answer» Correct Answer - A
992.

The temperature coefficient of resistance of a wire is 0.00125 per `.^oC`. At 300K, its resistance is 1 `Omega`. The resistance of the wire will be 2 `Omega` atA. `1154 K`B. `1100 K`C. `1500 K`D. `1127 K`

Answer» Correct Answer - D
(d) `(rho_(1))/(rho_(2)) = ((1 + alpha t_(1)))/((1 + alpha t_(2))) implies (1)/(2) = ((1 + 00125 xx 27))/((1 + 0.00125 xx t))`
`implies t = 854^(@)C implies T = 1127 K`
993.

The positive temperature coefficient of resistance is forA. CarbonB. GermaniumC. CopperD. An electrolyte

Answer» Correct Answer - C
994.

A resistance coil market is found to have a true resistance of `3.115 Omega` at `300 K`. Calculate the temperature at which marking is corrent .Temperature coefficient of resistance of the material of is `4.2xx 10^(-3).^(@)C^(-1)`

Answer» Correct Answer - `290.2K`
`t = 300 K = 300- 273 = 27^(@)C`
`R_(27) = R_(0)(1+ alpha xx 27)`
`R_(27) = R_(0)(1+ alpha xx 27)`……(i)
`:. 3.115 = R_(0) (1+ 4.3 xx 10^(-3) xx27)` ....(i)
and `3 = R_(0)(1+ 4.2 xx 10^(-3) xx t)`…..(ii)
`:. (3)/(3.115) = (1 + 4.2 xx 10^(-3) xx t)/(1+ 4.2 xx 10^(-3) xx 27)`
On solving we get `t = 17.21^(@)C`
`= 17.21 xx 275 = 290.2K`
995.

The temperature coefficient of resistance of a wire is 0.00125 per `.^oC`. At 300K, its resistance is 1 `Omega`. The resistance of the wire will be 2 `Omega` at

Answer» Correct Answer - `1127 K`
Here `alpha = 0.00125^(@)C^(-1)`
`t_(1) = 300 K= 300 - 273 = 27^(@)C`
`R_(27) = R_(0) (1 + alpha xx 27)`
and `R_(t) = R_(0) ( 1+alpha xx t)`
or `1 = R_(0) (1+ alpha xx 27) and 2 = R_(0) (1+ alpha t)`
`:. (2)/(1) (1+alpha t)/(1+alpha xx 27) or 1+ alpha t = 2+ 54 alpha`
or `t = (1+ 54 alpha)/(alpha) = (1+ 54 xx 0.00125)/(0.00125) = 854 ^(@)C`
`= 854 + 273 = 1127 K`
996.

A wire carries a current of 0.5A, when a potential differnece of 1.5 V is applied across it. What is its conductance ? If the wire is of length 3 m and area of cross-section `5.4 mm^(2)`, calculate its conductivity.

Answer» Here, `I=0.5 A , V=1.5 V, l=3 m`,
`A = 5.4 mm^(2) = 5.4 xx 10^(-6) m^(2)`
Now, resistance, `R=V/I=1.5/0.5 =3 Omega`
Conduction, `G=1/R=1/3=0.33 S`
Electrical conductivity, `sigma=1/rho =(l)/(RA)`
`=3/( 3xx 5.4 xx 10^(-6))=1.85 xx 10^(5) Sm^(-1)`
997.

A standard coil marked `5 Omega` is found to have a resistance of `5.128 Omega` at `30^@C`. Calculate the temperature at which the marking is correct. The temperature coefficient of resistance of the material of the coil is `.0042^@C^(-1)`.

Answer» `R_(t_1)=5Omega, R_(t_2)5.128 Omega`,
`t_(1)=?, t_(2)=30^@C`.
`R_(t_1)/R_(t_2)=(R_(0)(1+alpha t_(1)))/(R_(0)(1+alpha t_(2)))=(1 +alpha t_(1))/(1+alpha t_(2))`
or `5/5.128= (1+0.0042 xx t_(1))/(1+0.0042 xx30)`
On solving, `t_(1)=23.3^@C`
998.

A copper coil has resistance of `20.0 Omega` at `0^@C` and a resistance of `26.4 Omega` at `80^@C`. Find the temperature coefficient of resistance of copper.

Answer» Correct Answer - (i)` 6.45 xx 10^(-3)^(@)C^(-1)`(ii)` 0.267 Omega `(ii)`1.948 xx 10^(-4) Omega m`
Here,`r =1 mm = 10^(-3) , l = 50 cm = 0.50 m` ,
`R_(1)=0.31 Omega,t_(1)=25^(@)C,R_(2)=0.51 cm=0.50 m` ,
(i) Temperature coefficient of resistance
`alpha=(R_(2)-R_(1))/(R_(1)(t_(2)-t_(1)))=(0.51-0.31)/(0.31(125-25))`
`=(0.20)/(0.31xx100)=6.45xx10^(3).^(@)C^(-1)`
(ii) Resistance at `0^(@)C` is
`R_(0)=(R_(1))/(1+alphat_(1))=(0.31)/(1+(6.4xx10^(-3))xx25)=0.267^(@)Omega`
(iii) Resistivity at `0^(@)C`
`rho_(0)=(R_(0)A)/(l)=(R_(0)xxpir^(2))/(l)=(0.267xx3.142xx(10^(-3))^(2))/(0.50)`
`=1.68 xx 10^(-6)m`
Resistivity at `25^(@)C,rho_(25)=rho_(0)[1+alpha xx 25]`
`=1.68xx10^(-6)[1+6.4xx10^(-3)xx25]`
`=1.948xx10^(-6)Omegam`.
999.

The fact that the conductance of some metals rises to infinity at some temperature below a few Kelvin is calledA. Thermal conductivityB. Optical conductivityC. Magnetic conductivityD. Superconductivity

Answer» Correct Answer - D
1000.

At what temperature(in kelvin) would the resistance of a copper wire be half its resistance at `0^@C`? Temperature coefficient of resistance of copper is `3.9 xx 10^(-3).^(@)C^(-1)`.

Answer» Let at temperature `t^@C,R_(t)=1/2R_(0)`
Then `alpha=(R_(t) -R_(0))/(R_(0)xxt)=((R_(0)//2)-R_(0))/(R_()xxt) = -(1)/(2t)`
or `t = -(1)/(2 alpha) = - 1/( 2xx 3.9xx10^(-3))= -128.2^@C`
`=144.8K`