1
JEE Main 2022 (Online) 29th July Morning Shift
+4
-1

A coil of inductance 1 H and resistance $$100 \,\Omega$$ is connected to a battery of 6 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 ms after the circuit is switched on. (Given $$\ln 2=0.693, \mathrm{e}^{-3 / 2}=0.25$$)

A
t = 10 ms; U = 2 mJ
B
t = 10 ms; U = 1 mJ
C
t = 7 ms; U = 1 mJ
D
t = 7 ms; U = 2 mJ
2
JEE Main 2022 (Online) 28th July Evening Shift
+4
-1

A transformer operating at primary voltage $$8 \,\mathrm{kV}$$ and secondary voltage $$160 \mathrm{~V}$$ serves a load of $$80 \mathrm{~kW}$$. Assuming the transformer to be ideal with purely resistive load and working on unity power factor, the loads in the primary and secondary circuit would be

A
$$800 \,\Omega$$ and $$1.06 \,\Omega$$
B
$$10 \,\Omega$$ and $$500 \,\Omega$$
C
$$800 \,\Omega$$ and $$0.32 \,\Omega$$
D
$$1.06 \,\Omega$$ and $$500 \,\Omega$$
3
JEE Main 2022 (Online) 28th July Morning Shift
+4
-1

The equation of current in a purely inductive circuit is $$5 \sin \left(49\, \pi t-30^{\circ}\right)$$. If the inductance is $$30 \,\mathrm{mH}$$ then the equation for the voltage across the inductor, will be :

$$\left\{\right.$$ Let $$\left.\pi=\frac{22}{7}\right\}$$

A
$$1.47 \sin \left(49 \pi t-30^{\circ}\right)$$
B
$$1.47 \sin \left(49 \pi t+60^{\circ}\right)$$
C
$$23.1 \sin \left(49 \pi t-30^{\circ}\right)$$
D
$$23.1 \sin \left(49 \pi t+60^{\circ}\right)$$
4
JEE Main 2022 (Online) 27th July Evening Shift
+4
-1

A series LCR circuit has $$\mathrm{L}=0.01\, \mathrm{H}, \mathrm{R}=10\, \Omega$$ and $$\mathrm{C}=1 \mu \mathrm{F}$$ and it is connected to ac voltage of amplitude $$\left(\mathrm{V}_{\mathrm{m}}\right) 50 \mathrm{~V}$$. At frequency $$60 \%$$ lower than resonant frequency, the amplitude of current will be approximately :

A
466 mA
B
312 mA
C
238 mA
D
196 mA
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