1
JEE Main 2022 (Online) 27th July Morning Shift
Numerical
+4
-1

To light, a $$50 \mathrm{~W}, 100 \mathrm{~V}$$ lamp is connected, in series with a capacitor of capacitance $$\frac{50}{\pi \sqrt{x}} \mu F$$, with $$200 \mathrm{~V}, 50 \mathrm{~Hz} \,\mathrm{AC}$$ source. The value of $$x$$ will be ___________.

2
JEE Main 2022 (Online) 26th July Morning Shift
Numerical
+4
-1

The effective current I in the given circuit at very high frequencies will be ___________ A.

3
JEE Main 2022 (Online) 30th June Morning Shift
Numerical
+4
-1

A series LCR circuit with $$R = {{250} \over {11}}\,\Omega$$ and $${X_L} = {{70} \over {11}}\,\Omega$$ is connected across a 220 V, 50 Hz supply. The value of capacitance needed to maximize the average power of the circuit will be _________ $$\mu$$F. (Take : $$\pi = {{22} \over 7}$$)

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

An inductor of 0.5 mH, a capacitor of 200 $$\mu$$F and a resistor of 2 $$\Omega$$ are connected in series with a 220 V ac source. If the current is in phase with the emf, the frequency of ac source will be ____________ $$\times$$ 102 Hz.