Current Electricity · JEE Main previous year questions

An inductor stores 16 J of magnetic field energy and dissipates 32 W of thermal energy due to its resistance when an a.c. current of 2 A (rms) and frequency 50 Hz flows through it. The ratio of inductive reactance to its resistance is ________. $(\pi =3.14)$

Two resistors of $100\Omega$ each are connected in series with a $9\mathrm{V}$ battery. A voltmeter of $400\Omega$ resistance is connected to measure the voltage drop across one of the resistors. The voltmeter reading is ____ V.

1. A.3
2. B.2
3. C.4
4. D.4.5

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

A voltage regulating circuit consisting of Zener diode, having break-down voltage of $10\mathrm{V}$ and maximum power dissipation of $0.4\mathrm{W}$ , is operated at $15\mathrm{V}$ . The approximate value of protective resistance in this circuit is ____ $\Omega$ .

1. A.$(\pi +1)2r\lambda$
2. B.$\frac{6\pi \lambda r}{3\pi +16}$
3. C.$\frac{3\pi \lambda r}{8}$
4. D.$2\pi \lambda r$

Suppose a long solenoid of $100\text{ cm}$ length, radius $2\text{ cm}$ having $500$ turns per unit length, carries a current $I=10\sin (\omega t)\text{A}$, where $\omega =1000\text{rad. /s}$. A circular conducting loop $(B)$ of radius $1\text{ cm}$ coaxially slided through the solenoid at a speed $v=1\text{ cm/s}$. The r.m.s. current through the loop when the coil $B$ is inserted $10\text{ cm}$ inside the solenoid is $\frac{\alpha }{\sqrt{2}}\mu \text{A}$. The value of $\alpha$ is _____. [Resistance of the loop $=10\Omega$ ]

1. A.80
2. B.280
3. C.100
4. D.197

1. A.$\frac{mgR}{B^2{l}^2}$
2. B.$\frac{2mgR}{B^2{L}^2}$
3. C.$\frac{2mgR}{B^2{l}^2}$
4. D.$\frac{8mgR}{B^2{l}^2}$

1. A.$R_2=8\Omega ,R_1=\frac{16}{3}\Omega$
2. B.$R_2=12\Omega ,R_1=\frac{12}{3}\Omega$
3. C.$R_2=4\Omega ,R_1=\frac{4}{3}\Omega$
4. D.$R_2=16\Omega ,R_1=\frac{16}{3}\Omega$

Inductance of a coil with $10^4$ turns is 10 mH and it is connected to a dc source of 10 V with internal resistance of $10\Omega$. The energy density in the inductor when the current reaches $\left(\frac{1}{e}\right)$ of its maximum value is $\alpha \pi \times \frac{1}{e^2}J/{\mathrm{m}}^3$. The value of $\alpha$ is ____. $\left({\mu }_0=4\pi \times 10^{-7}Tm/A\right)$.

1. A.NOR gate
2. B.OR gate
3. C.AND gate
4. D.NAND gate

1. A.$5.7\times 10^{-2}$
2. B.$7.5\times 10^{-3}$
3. C.$5.7\times 10^{-3}$
4. D.$7.5\times 10^{-2}$

1. A.$2(\sqrt{3}-1)R$
2. B.$R$
3. C.$(\sqrt{3}-1)R$
4. D.$(\sqrt{3}+1)R$

1. A.25
2. B.30
3. C.15
4. D.20

A battery with EMF $E$ and internal resistance $r$ is connected across a resistance $R$. The power consumption in $R$ will be maximum when:

1. A.$R=\sqrt{2}r$
2. B.$R=2r$
3. C.$R=\frac{r}{2}$
4. D.$R=r$

1. A.$\frac{2{\mu }_{0}I}{3\pi a}$
2. B.$\frac{\sqrt{2}{\mu }_{0}I}{3\pi a}$
3. C.$\frac{3\pi {\mu }_{0}I}{\sqrt{2}a}$
4. D.$\frac{{\mu }_{0}I}{2\pi a}$

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

A wire of length $25\mathrm{m}$ and cross-sectional area $5\mathrm{m}{\mathrm{m}}^2$ having resistivity of $2\times 10^{-6}\Omega \mathrm{m}$ is bent into a complete circle. The resistance between diametrically opposite points will be

1. A.$100\Omega$
2. B.$2.5\Omega$
3. C.$12.5\Omega$
4. D.$50\Omega$

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

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

Two cells of emfs $1\mathrm{V}$ and $2\mathrm{V}$ and internal resistances $2\Omega$ and $1\Omega$, respectively, are connected in series with an external resistance of $6\Omega$. The total current in the circuit is $I_1$. Now the same two cells in parallel configuration are connected to same external resistance. In this case, the total current drawn is $I_2$. The value of $\left(\frac{I_1}{I_2}\right)$ is $\frac{x}{3}$. The value of $x$ is__________.

The battery of a mobile phone is rated as $4.2\text{ V},5800\text{ mAh}$. How much energy is stored in it when fully charged?

1. A.87.7 kJ
2. B.43.8 kJ
3. C.48.7 kJ
4. D.24.4 kJ

A zener diode with $5\text{ V}$ zener voltage is used to regulate an unregulated dc voltage input of $25\text{ V}$. For a $400\Omega$ resistor connected in series, the zener current is found to be 4 times load current. The load current ($I_{\mathrm{L}}$) and load resistance ($R_{\mathrm{L}}$) are :

1. A.$I_{\mathrm{L}}=0.02\text{ mA};R_{\mathrm{L}}=250\Omega$
2. B.$I_{\mathrm{L}}=10\text{ A};R_{\mathrm{L}}=0.5\Omega$
3. C.$I_{\mathrm{L}}=10\text{ mA};R_{\mathrm{L}}=500\Omega$
4. D.$I_{\mathrm{L}}=20\text{ mA};R_{\mathrm{L}}=250\Omega$

1. A.$P=0,Q=1$
2. B.$P=1,Q=0$
3. C.$P=0,Q=0$
4. D.$P=1,Q=1$