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

A circuit element $$\mathrm{X}$$ 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 $$\mathrm{Y}$$ 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 $$\mathrm{X}$$ and $$\mathrm{Y}$$ are connected in series to the same supply, what will be the rms value of the current in ampere?

A
$$\frac{10}{\sqrt{2}}$$
B
$$\frac{5}{\sqrt{2}}$$
C
$$5 \sqrt{2}$$
D
$$\frac{5}{2}$$
2
JEE Main 2022 (Online) 29th July Morning Shift
+4
-1

An alternating emf $$\mathrm{E}=440 \sin 100 \pi \mathrm{t}$$ 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 :

A
4.4 A
B
1.55 A
C
2.2 A
D
3.11 A
3
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
4
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 $$500 \,\Omega$$
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