An inductor of $10$ mH, capacitor of $0.1\ \mu$F and a resistor of $100\ \Omega$ are connected in series across an $a.c$ power supply $220$ V, $70$ Hz. The power factor of the given circuit is $0.5$. The difference in the inductive reactance and capacitance reactance is $\sqrt3\,\alpha\ \Omega$. The value of $\alpha$ is ______.

JEE Main 2026 · PhysicsNumerical answerNumerical valueMediumCalculation

JEE Main 4 April 2026, Shift 1, Physics Q50

Question 50 of 75 in this shift, Physics question 25 of 25, Section B.

An inductor of

10

mH, capacitor of

0.1\ \mu

F and a resistor of

100\ \Omega

are connected in series across an

a.c

power supply

220

70

Hz. The power factor of the given circuit is

0.5

. The difference in the inductive reactance and capacitance reactance is

\sqrt3\,\alpha\ \Omega

. The value of

\alpha

is ______.

Official answer

100

NTA final key.

Chapter: Alternating Current
Topic: Phasor Diagrams
Idea tested: Impedance Triangle Construction

Same idea in other shifts

Asked 9× in all

2 Apr 2026, Shift 2 · Q42The figure given below shows an LCR series circuit with two switches $S_1$ and $S_2$ . When switch $S_1$ is closed keeping $S_2$ open, the…HardSingle correctHas a figure
5 Apr 2026, Shift 1 · Q44An a.c. source of angular frequency $\omega$ is connected across a resistor $R$ and a capacitor $C$ in series. The current is observed as…MediumSingle correct
5 Apr 2024, Shift 1 · Q57An ac source is connected in given series LCR circuit. The rms potential difference across the capacitor of $20\ \mu\mathrm{F}$ is…MediumNumerical valueHas a figure
9 Apr 2024, Shift 1 · Q43A bulb and a capacitor are connected in series across an ac supply. A dielectric is then placed between the plates of the capacitor. The…MediumSingle correct
27 Jul 2022, Shift 2 · Q44A series LCR circuit has L = 0.01 H, R = 10 $\Omega$ and C = 1 $\mu$ F and it is connected to ac voltage of amplitude ( $\mathrm{V_m}$ ) 50…MediumSingle correct
25 Jun 2022, Shift 2 · Q42A sinusoidal voltage $V(t)$ = 210 sin 3000 $t$ volt is applied to a series LCR circuit in which $L$ = 10 $mH$ , $C$ =25 µ $F$ and $R$ = 100…MediumSingle correct
28 Jun 2022, Shift 1 · Q54An AC source is connected to an inductance of 100 mH, a capacitance of 100 $\mu$ F and a resistance of 120 $\Omega$ as shown in figure.…MediumNumerical valueHas a figure
3 Sep 2020, Shift 1 · Q15A 750 Hz, 20 V (rms) source is connected to a resistance of 100 $\Omega$ , an inductance of 0.1803 H and a capacitance of 10 $\mu$ F all in…MediumSingle correct

Question text from the official JEE Main paper published by NTA; answer from the final answer key. Chapter, topic and idea tags, difficulty and skill are Lumi’s. Lumi analyses 108 of the 174 JEE Main shifts held from 2017 to 2026.