1
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
$$23.1 \sin \left(49 \pi t+60^{\circ}\right)$$
2
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
3
JEE Main 2022 (Online) 27th July Morning Shift
+4
-1

A direct current of $$4 \mathrm{~A}$$ and an alternating current of peak value $$4 \mathrm{~A}$$ 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 :

A
3 : 2
B
3 : 1
C
3 : 4
D
4 : 3
4
JEE Main 2022 (Online) 26th July Morning Shift
+4
-1

In a series $$L R$$ circuit $$X_{L}=R$$ and power factor of the circuit is $$P_{1}$$. When capacitor with capacitance $$C$$ such that $$X_{L}=X_{C}$$ is put in series, the power factor becomes $$P_{2}$$. The ratio $$\frac{P_{1}}{P_{2}}$$ is:

A
$$\frac{1}{2}$$
B
$$\frac{1}{\sqrt{2}}$$
C
$$\frac{\sqrt{3}}{\sqrt{2}}$$
D
2 : 1
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