Current Electricity · JEE Main previous year questions

A null point is found at 200 cm in potentiometer when cell in secondary circuit is shunted by $5\Omega$. When a resistance of $15\Omega$ is used for shunting, null point moves to 300 cm. The internal resistance of the cell is __________$\Omega$.

A uniform metallic wire carries a current 2 A, when 3.4 V battery is connected across it. The mass of uniform metallic wire is $8.92\times 10^{-3}\mathrm{kg}$, density is $8.92\times 10^{3}kg/{\mathrm{m}}^3$ and resistivity is $1.7\times 10^{-8}\Omega \text{-}\mathrm{m}$. The length of wire is :

1. A.$l=100\mathrm{m}$
2. B.$l=6.8\mathrm{m}$
3. C.$l=5\mathrm{m}$
4. D.$l=10\mathrm{m}$

An LCR series circuit of capacitance 62.5 nF and resistance of $50\Omega$, is connected to an A.C. source of frequency 2.0 kHz. For maximum value of amplitude of current in circuit, the value of inductance is ____ mH. (Take ${\pi }^2=10$)

The resistance of a wire is $5\Omega$. Its new resistance in ohm if stretched to 5 times of its original length will be :

1. A.25
2. B.625
3. C.5
4. D.125

1. A.${\mathrm{I}}_4=\frac{8}{5}\mathrm{A}$ and ${\mathrm{I}}_5=\frac{2}{5}\mathrm{A}$
2. B.${\mathrm{I}}_4=\frac{6}{5}\mathrm{A}$ and ${\mathrm{I}}_5=\frac{24}{5}\mathrm{A}$
3. C.${\mathrm{I}}_4=\frac{2}{5}\mathrm{A}$ and ${\mathrm{I}}_5=\frac{8}{5}\mathrm{A}$
4. D.${\mathrm{I}}_4=\frac{24}{5}\mathrm{A}$ and ${\mathrm{I}}_5=\frac{6}{5}\mathrm{A}$

A hollow cylindrical conductor has length of $3.14\mathrm{m}$, while its inner and outer diameters are $4\mathrm{mm}$ and $8\mathrm{mm}$ respectively. The resistance of the conductor is $n\times 10^{-3}\Omega$. If the resistivity of the material is $2.4\times 10^{-8}\Omega \mathrm{m}$, the value of $n$ is ____.

A cell of emf 90 V is connected across series combination of two resistors each of $100\Omega$ resistance. A voltmeter of resistance $400\Omega$ is used to measure the potential difference across each resistor. The reading of the voltmeter will be :

1. A.40 V
2. B.90 V
3. C.45 V
4. D.80 V

If a copper wire is stretched to increase its length by 20%. The percentage increase in resistance of the wire is __________%.

An alternating emf $\mathrm{E}=440\sin 100\pi t$ is applied to a circuit containing an inductance of $\frac{\sqrt{2}}{\pi }\mathrm{H}$. If an a.c. ammeter is connected in the circuit, its reading will be :

1. A.$4.4\mathrm{A}$
2. B.$1.55\mathrm{A}$
3. C.$2.2\mathrm{A}$
4. D.$3.11\mathrm{A}$

A coil of inductance $1\mathrm{H}$ and resistance $100\Omega$ is connected to a battery of $6\mathrm{V}$. Determine approximately : (a) The time elapsed before the current acquires half of its steady - state value. (b) The energy stored in the magnetic field associated with the coil at an instant $15\mathrm{ms}$ after the circuit is switched on. (Given $\ln 2=0.693,{\mathrm{e}}^{-3/2}=0.25$)

1. A.$\mathrm{t}=10\mathrm{ms};\mathrm{U}=2\mathrm{mJ}$
2. B.$\mathrm{t}=10\mathrm{ms};\mathrm{U}=1\mathrm{mJ}$
3. C.$\mathrm{t}=7\mathrm{ms};\mathrm{U}=1\mathrm{mJ}$
4. D.$\mathrm{t}=7\mathrm{ms};\mathrm{U}=2\mathrm{mJ}$

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R. Assertion A: Alloys such as constantan and manganin are used in making standard resistance coils. Reason R: Constantan and manganin have very small value of temperature coefficient of resistance. In the light of the above statements, choose the correct answer from the options given below.

1. A.Both A and R are true and R is the correct explanation of A.
2. B.Both A and R are true but R is NOT the correct explanation of A.
3. C.A is true but R is false.
4. D.A is false but R is true.

A $1\mathrm{m}$ long wire is broken into two unequal parts X and Y. The X part of the wire is streched into another wire W. Length of $W$ is twice the length of $X$ and the resistance of W is twice that of Y. Find the ratio of length of X and Y.

1. A.$1:4$
2. B.$1:2$
3. C.$4:1$
4. D.$2:1$

A circuit element X when connected to an a.c. supply of peak voltage $100\mathrm{V}$ gives a peak current of $5\mathrm{A}$ which is in phase with the voltage. A second element Y when connected to the same a.c. supply also gives the same value of peak current which lags behind the voltage by $\frac{\pi }{2}$. If X and Y are connected in series to the same supply, what will be the rms value of the current in ampere?

1. A.$\frac{10}{\sqrt{2}}$
2. B.$\frac{5}{\sqrt{2}}$
3. C.$5\sqrt{2}$
4. D.$\frac{5}{2}$

A wire of resistance ${\text{R}}_1$ is drawn out so that its length is increased by twice of its original length. The ratio of new resistance to original resistance is :

1. A.$9:1$
2. B.$1:9$
3. C.$4:1$
4. D.$3:1$

The frequencies at which the current amplitude in an LCR series circuit becomes $\frac{1}{\sqrt{2}}$ times its maximum value, are $212{\text{ rad s}}^{-1}$ and $232{\text{ rad s}}^{-1}$. The value of resistance in the circuit is $R=5\Omega$. The self inductance in the circuit is _________ $\text{mH}$.

Given below are two statements : Statement I : A uniform wire of resistance $80\Omega$ is cut into four equal parts. These parts are now connected in parallel. The equivalent resistance of the combination will be $5\Omega$. Statement II: Two resistances 2R and 3R are connected in parallel in an electric circuit. The value of thermal energy developed in 3R and 2R will be in the ratio $3:2$. In the light of the above statements, choose the most appropriate answer from the option given below

1. A.Both statement I and statement II are correct
2. B.Both statement I and statement II are incorrect
3. C.Statement I is correct but statement II is incorrect
4. D.Statement I is incorrect but statement II is correct

Two sources of equal emfs are connected in series. This combination is connected to an external resistance R. The internal resistances of the two sources are $r_1$ and $r_2$ ($r_1>r_2$). If the potential difference across the source of internal resistance $r_1$ is zero, then the value of R will be :

1. A.$r_1-r_2$
2. B.$\frac{r_1{r}_2}{r_1+r_2}$
3. C.$\frac{r_1+r_2}{2}$
4. D.$r_2-r_1$

A direct current of $4\text{ A}$ and an alternating current of peak value $4\text{ A}$ flow through resistance of $3\Omega$ and $2\Omega$ respectively. The ratio of heat produced in the two resistances in same interval of time will be :

1. A.$3:2$
2. B.$3:1$
3. C.$3:4$
4. D.$4:3$