NEET Physics Current Electricity MCQs Set 05

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Chapter-wise Objective Questions: Current Electricity

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Practise 25 chapter-wise NEET Physics questions on Current Electricity in this set, each with a worked solution you can open after attempting it. The questions test Ohm's law, resistivity, combinations of resistors, Kirchhoff's laws, cells, the potentiometer and the Wheatstone bridge.

Question 1: A voltmeter having resistance of \(50×{10}^{3} ohm\) is used to measure the voltage in a circuit. To increase the range of measurement 3 times the additional series resistance required is
(a) \({10}^{5} ohm\)
(b) \(150 k.ohm\)
(c) \(900 k.ohm\)
(d) \(9×{10}^{6}ohm\)
Show Answer & Explanation

Answer: (a) \({10}^{5} ohm\)

Explanation:
1. \(R=G\left(n-1\right)=50×{10}^{3}\left(3-1\right)={10}^{5}Ω\)

Question 2: A wire of resistance R is divided in 10 equal parts. These parts are connected in parallel, the equivalent resistance of such connection will be
(a) \(0.01 R\)
(b) \(0.1 R\)
(c) \(10 R\)
(d) \(100 R\)
Show Answer & Explanation

Answer: (a) \(0.01 R\)

Explanation:
1. Each part will have a resistance \(r=R/10\)
2. Let equivalent resistance be \({r}_{R},\) then
3. \(\frac{1}{{r}_{R}}=\frac{1}{r}+\frac{1}{r}+\frac{1}{r}…….\) 10 times
4. \(∴\frac{1}{{r}_{R}}=\frac{10}{r}=\frac{10}{R/10}=\frac{100}{R}⇒{r}_{R}=\frac{R}{100}=0.01R\)

Question 3: A certain wire has a resistance \(R.\) The resistance of another wire identical with the first except having twice its diameter is
(a) \(2 R\)
(b) \(0.25 R\)
(c) \(4 R\)
(d) \(0.5 R\)
Show Answer & Explanation

Answer: (b) \(0.25 R\)

Explanation:
1. \(R∝\frac{1}{A}⇒R∝\frac{1}{{r}^{2}}∝\frac{1}{{d}^{2}}\) [\(d=\)diameter of wire]

Question 4: The resistance of a wire at 300 K is found to be 0.3\(Ω\). If the temperature coefficient of
resistance of wire is \(1.5×{10}^{-3}{K}^{-1}\) , the temperature at which the resistance becomes 0.6\(Ω\) is
(a) 720 K
(b) 345 K
(c) 993 K
(d) 690 K
Show Answer & Explanation

Answer: (c) 993 K

Explanation:
1. Given, \({R}_{300}=0.3Ω, {R}_{t}=0.6Ω\)
2. \(T=300K=27°C\)
3. Temperature coefficient of resistance,
4. \(α=1.5×{10}^{-3}{K}^{-1}\)
5. \(∴{R}_{300}={R}_{0}\left(1+α×27\right)\)
6. \(0.3={R}_{0}\left(1+1.5×{10}^{-3}×27\right) …\left(i\right)\)
7. Again, \({R}_{t}={R}_{0}\left(1+αt\right)\)
8. \(0.6={R}_{0}\left(1+×{10}^{-3}×t\right) …\left(\mathrm{ii}\right)\)
9. Dividing Eq. (ii) by Eq. (i), we get
10. \(\frac{0.6}{0.3}=\frac{1+1.5×{10}^{-3}t}{1+1.5×{10}^{-3}×27 }\)
11. \(⟹2\left(1+1.5×{10}^{-3}×27\right)=1+1.5×{10}^{-3}t\)
12. \(⟹2+81×{10}^{-3}=1+1.5×{10}^{-3}t\)
13. \(⟹2+0.081=1+1.5×{10}^{-3}t\)
14. \(⟹t=\frac{1.081}{1.5×{10}^{-3}}=720°C=993K\)

Question 5: The Petlier coefficient of a thermo-couple of metls\(A\)and \(B\) at junction temperature \(T\) is given by
(a) \({T}^{2}\frac{dE}{d{T}^{2}}\)
(b) \(T\frac{dE}{dT}\)
(c) \({T}^{3}\frac{d{E}^{2}}{dT}\)
(d) \({T}^{4}\frac{{d}^{2}E}{d{T}^{2}}\)
Show Answer & Explanation

Answer: (b) \(T\frac{dE}{dT}\)

Explanation:
1. \(π=T dE/dT\).

Question 6: Find the true statements
(a) Ohm’s law is applicable to all conductors of electricity
(b) In an electrolyte solution, the electric current is mainly due to the movement of electrons
(c) The resistance of an incandescent lamp is lesser when the lamp is switched on
(d) Specific resistance of a wire depends upon its dimension
Show Answer & Explanation

Answer: (c) The resistance of an incandescent lamp is lesser when the lamp is switched on

Explanation:
1. The temperature coefficient of the carbon is negative so the resistance of carbon decreases with the increase of temperature.

Question 7: A wire of resistance \(R\) is cut into \('n'\) equal parts. These parts are then connected in parallel. The equivalent resistance of the combination will be
(a) \(nR\)
(b) \(\frac{R}{n}\)
(c) \(\frac{n}{R}\)
(d) \(\frac{R}{{n}^{2}}\)
Show Answer & Explanation

Answer: (d) \(\frac{R}{{n}^{2}}\)

Explanation:
1. Resistance of each part will be \(\frac{R}{n};\) such \(n\) parts are joined in parallel so \({R}_{eq}=\frac{R}{{n}^{2}}\)

Question 8: A potential difference of \(V\) is applied at the ends of a copper wire of length \(l\) and diameter \(d\). On doubling only \(d\), the drift velocity,
(a) Becomes two times
(b) Becomes half
(c) Does not change
(d) Becomes one-fourth
Show Answer & Explanation

Answer: (c) Does not change

Explanation:
1. \({v}_{d}=\frac{I}{nAl}=\frac{1}{nAe}×\frac{V}{R}\)
2. \(=\frac{1}{nAe}×\frac{V}{(ρl/A)}=\frac{V}{neρl}\)
3. As \({v}_{d}\) is independent of area of cross-section hence drift velocity will not change, when diameter is doubled

Question 9: On passing the current in water voltmeter, hydrogen
(a) Is liberated at anode
(b) Is liberated at cathode
(c) Is not liberated
(d) Remains in the solution
Show Answer & Explanation

Answer: (b) Is liberated at cathode

Explanation:
1. Because \(H\) has positive charge

Question 10: The cold junction of a thermocouple is maintained at \(10℃.\) No thermo \(e\).m.f. is developed when the hot junction is maintained at \(530℃.\) The neutral temperature is
(a) \(260℃\)
(b) \(270℃\)
(c) \(265℃\)
(d) \(520℃\)
Show Answer & Explanation

Answer: (b) \(270℃\)

Explanation:
1. \({T}_{n}=\frac{{T}_{i}+{T}_{c}}{2}=\frac{10+530}{2}=270℃\)

Question 11: A brass rectangular plate \(\mathrm{12cm×3cm}\) is to be electroplated with copper. If we wish to coat it with a layer of 0.02 mm thick both sides, how much time will it take with a constant current of 5A? Given ECE of copper is \(33×{10}^{-5}g{ C}^{-1}\) and density of copper is \(8.9 g c{m}^{-3}.\)
(a) 388 s
(b) 776 s
(c) 400 s
(d) 800 s
Show Answer & Explanation

Answer: (b) 776 s

Explanation:
1. Mass of copper deposited,
2. \(m=\mathrm{volume×density}\)
3. \(=(\mathrm{area×thickness)×density}\)
4. \(=[2×(12×3)×0.002]×8.9\) g
5. \(t=\frac{m}{zI}=\frac{[2(12×3)×0.002×8.91]}{33×{10}^{-5}×5}=776\)s.

Question 12: The \(V-i\) graph for a good conductor makes angle \(40°\) with \(V-\)axis. Here \(V\) denotes voltage and \(i\) denotes current. The resistance of the conductor will be
(a) \(\mathrm{sin}\,40°\)
(b) \(\mathrm{cos}\,40°\)
(c) \(\mathrm{tan}\,40°\)
(d) \(\mathrm{cot}\,40°\)
Show Answer & Explanation

Answer: (d) \(\mathrm{cot}\,40°\)

Explanation:
1. Resistance, \(R=\frac{V}{i}=\mathrm{cot}\,40°\)

Question 13: If the resistivity of an alloy is \(ρ'\) and that of constituent metal is \(ρ\) then
(a) \(ρ\)’>\(ρ\)
(b) \(ρ\)’<\(ρ\)
(c) \({ρ}^{'}= ρ\)
(d) There is no simple relation between\(ρ\) and \({ρ}^{'}\)
Show Answer & Explanation

Answer: (a) \(ρ\)’>\(ρ\)

Explanation:
1. The resistivity of metal increases when it is converted into an alloy
2. \(∴ {ρ}^{'}>ρ\)

Question 14: A current of 0.01mA passes through the potentiometer wire of a resistivity of
\({10}^{9}Ω\)-cm and area of cross-section \({10}^{-2}c{m}^{2}\). The potential gradient is
(a) \({10}^{9}V{m}^{-1}\)
(b) \({10}^{11}V{m}^{-1}\)
(c) \({10}^{10}V{m}^{-1}\)
(d) \({10}^{8}V{m}^{-1}\)
Show Answer & Explanation

Answer: (d) \({10}^{8}V{m}^{-1}\)

Explanation:
1. Potential gradient is given by
2. \(k=\frac{V}{l}=\frac{IR}{l}\left(∵V=I R\right)\)
3. \(=\frac{I×ρl/A}{l}\left(∵R=\frac{ρl}{A}\right)\)
4. \(=\frac{Iρ}{A}\)
5. \(∴ k=\frac{0.01×{10}^{-3}×{10}^{9}×{10}^{-2}}{{10}^{-2}×{10}^{-4}}={10}^{8}V{m}^{-1}\)

Question 15: A heating coil can heat the water of a vessel from \(20℃\) to \(60℃\) in \(30 minutes.\) Two such heating coils are put in series and then used to heat the same amount of water through the same temperature range. The time taken now will be (neglecting thermal capacity of the coils)
(a) \(60 minutes\)
(b) \(30 minutes\)
(c) \(15 minutes\)
(d) \(7.5 minutes\)
Show Answer & Explanation

Answer: (a) \(60 minutes\)

Explanation:
1. \({H}_{1}={H}_{2}⇒\frac{{v}^{2}}{R}{t}_{1}=\frac{{v}^{2}}{2R}{t}_{2}⇒{t}_{2}=2{t}_{1}⇒{t}_{1}=30 \mathrm{min}\)
2. \(∴{t}_{2}=60 \mathrm{min}\)

Question 16: \(A, B, C\)and\(D\) are four resistances of \(2Ω, 2Ω, 2\mathrm{Ωand} 3Ω\) respectively. They are used to form a Wheatstone bridge. The resistance \(D\) is short circuted with a resistances R in order to get the bridge balanced. The value of \(R\) will be
(a) \(4 Ω\)
(b) \(6 Ω\)
(c) \(8 Ω\)
(d) \(3 Ω\)
Show Answer & Explanation

Answer: (b) \(6 Ω\)

Explanation:
1. The bridge will be balanced when the shunted resistance of value \(2Ω ie, 2=\frac{3×S}{3+S}\). On solving \(S=6 Ω\)

Question 17: A copper voltmeter is connected in series with a heater coil of resistance \(0.1Ω.\) A steady current flows in the circuit for twenty minutes and mass of \(0.99 g\) of copper is deposited at the cathode. If electrochemical equivalent of copper is \(0.00033 gm/C,\) then heat generated in the coil is
(a) \(750 J\)
(b) \(650 J\)
(c) \(350 J\)
(d) \(250 J\)
Show Answer & Explanation

Answer: (a) \(750 J\)

Explanation:
1. \(m=Zi t ⇒i=\frac{m}{Zt}=\frac{0.99}{0.00033×1200}=2.5A\)
2. Hence heat generated in the coil is
3. \(H={i}^{2}Rt={\left(2.5\right)}^{2}×0.1×1200=750 J\)

Question 18: In water voltmeter, the electrolysis of …… takes place
(a) \({H}_{2}O\)
(b) \({H}_{2}S{O}_{4}\)
(c) \({H}_{2}O \mathrm{and}{H}_{2}S{O}_{4}\mathrm{both}\)
(d) \({H}_{2}\)and \({O}_{2}\)
Show Answer & Explanation

Answer: (a) \({H}_{2}O\)

Explanation:
1. Because \({H}_{2}O\) is used as electrolyte

Question 19: Water boils in an electric kettle in \(15 minutes\) after switching on. If the length of the heating wire is decreased to 2/3 of its initial value, then the same amount of water will boil with the same supply voltage in
(a) \(15 minutes\)
(b) \(12 minutes\)
(c) \(10 minutes\)
(d) \(8 minutes\)
Show Answer & Explanation

Answer: (c) \(10 minutes\)

Explanation:
1. \(H=\frac{{V}^{2}}{R}t\)
2. Since supply voltage is same and equal amount of heat is produced, therefore
3. \(\frac{{R}_{1}}{{t}_{1}}=\frac{{R}_{2}}{{t}_{2}}\mathrm{or}\frac{{R}_{1}}{{R}_{2}}=\frac{{t}_{1}}{{t}_{2}} …(i)\)
4. But\(R∝l⇒\frac{{R}_{1}}{{R}_{2}}=\frac{{l}_{1}}{{l}_{2}}\)…(ii)
5. By (i) and (ii)\(, \frac{{l}_{1}}{{l}_{2}}=\frac{{t}_{1}}{{t}_{2}}\)…(iii)
6. Now\({l}_{2}=\frac{2}{3}{l}_{1}⇒\frac{{l}_{1}}{{l}_{2}}=\frac{3}{2}\)
7. \(∴\) By equation\(\left(\mathrm{iii}\right),\frac{3}{2}=\frac{15}{{t}_{2}}⇒{t}_{2}=10 minutes\)

Question 20: All the edges of a block with parallel faces are unequal. Its tangent edge is twice its shortest edge. The ratio of the maximum to minimum resistance between parallel faces is
(a) 8
(b) 4
(c) 2
(d) None of these
Show Answer & Explanation

Answer: (b) 4

Explanation:
1. Let the length of various edges in increase order be\(l,x,2l\) respectively
2. \({R}_{\mathrm{max}}=\frac{ρ2l}{xl}=\frac{2ρ}{x};{R}_{\mathrm{min}}=\frac{ρl}{2lx}=\frac{ρ}{2x}\)
3. \(∴ \frac{{R}_{\mathrm{max}}}{{R}_{\mathrm{min}}}=4\)

Question 21: The internal resistance of a primary cell is 4\(Ω\) . It generates a current of 0.2 A in an external resistance of 21 \(Ω\). The rate at which chemical energy is consumed in providing the current is
(a) 0.42 J \({s}^{-1}\)
(b) 0.84 J \({s}^{-1}\)
(c) 1 J \({s}^{-1}\)
(d) 5 J \({s}^{-1}\)
Show Answer & Explanation

Answer: (c) 1 J \({s}^{-1}\)

Explanation:
1. Chemical energy consumed per sec = heat energy produced per sec.
2. \({I}^{2}\left(R+r\right)={\left(0.2\right)}^{2}\left(21+4\right)=1 J {s}^{-1}\)

Question 22: Two cells, each of \(e.m.f. E\) and internal resistance \(r\) are connected in parallel between the resistance \(R.\) The maximum energy given to the resistor will be, only when
(a) \(R=r/2\)
(b) \(R=r\)
(c) \(R=2r\)
(d) \(R=0\)
Show Answer & Explanation

Answer: (a) \(R=r/2\)

Explanation:
1. For maximum energy, we have
2. External resistance of the circuit
3. =Equivalent internal resistance of the circuit \(i.e. R=\frac{r}{2}\)

Question 23: The length of the wire is doubled. Its conductance will be
(a) Unchanged
(b) Halved
(c) Quadrupled
(d) 1/4 of the original value
Show Answer & Explanation

Answer: (b) Halved

Explanation:
1. Conductance \(C=\frac{1}{R}=\frac{A}{ρl}⇒C∝\frac{1}{l}\)

Question 24: The effective resistance of two resistors in parallel is \(\frac{12}{7}Ω.\) If one of the resistors is disconnected the resistance becomes \(4 Ω.\) The resistance of the other resistor is
(a) \(4 Ω\)
(b) \(3 Ω\)
(c) \(\frac{12}{7} Ω\)
(d) \(\frac{7}{12} Ω\)
Show Answer & Explanation

Answer: (b) \(3 Ω\)

Explanation:
1. \(\frac{7}{12}=\frac{1}{4}+\frac{1}{R}⇒R=3Ω\)

Question 25: If \(2.2kW\) power is transmitted through a \(100Ω\) line at \(22,000V,\) the power loss in the form of heat will be
(a) \(0.1 W\)
(b) \(1 W\)
(c) \(10 W\)
(d) \(100 W\)
Show Answer & Explanation

Answer: (b) \(1 W\)

Explanation:
1. \(P=Vi⇒i=\frac{2.2×{10}^{3}}{22000}=\frac{1}{10}A\)
2. \(\mathrm{Now\ loss\ of\ power=}{i}^{2}R={\left(\frac{1}{10}\right)}^{2}×100=1 W\)

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