Student Login

Home›Chapters›Alternating Current PYQs›Power, Power Factor & Wattless Current›Question 57

JEE Main 2021 (27 Aug, Shift 2) · Power, Power Factor & Wattless Current

Power, Power Factor & Wattless Current question from JEE Main 2021 (27 Aug, Shift 2)

Q57JEE Main 2021 · 27 AUG · SHIFT 2Medium

Power, Power Factor & Wattless Current

An ac circuit has an inductor and a resistor of resistance R in series, such that XL = 3R. Now, a capacitor is added in series such that XC = 2R. The ratio of new power factor with the old power factor of the circuit is $\sqrt{5}:x$ . The value of x is ___________.

Numerical answer type. Work it out, then open the answer.

Show answer and solution

Answer: 1

Old: $Z=\sqrt{R^2+9R^2}=\sqrt{10}R$ , $\cos\phi_1 = 1/\sqrt{10}$ .
New: $X = 3R-2R = R$ , $Z=\sqrt{2}R$ , $\cos\phi_2 = 1/\sqrt{2}$ .
$\frac{\cos\phi_2}{\cos\phi_1} = \frac{\sqrt{10}}{\sqrt{2}} = \sqrt{5}:1$
So $x = 1$ .

Report a mistake

More questions on Power, Power Factor & Wattless Current

Two circuits are shown in the figure (a) & (b). At a frequency of ____________ rad/s the…JEE Main 2021 (25 Jul, Shift 2)
A series LCR circuit driven by 300 V at a frequency of 50 Hz contains a resistance R = 3…JEE Main 2021 (26 Aug, Shift 1)
An LCR circuit contains resistance of 110 Ω and a supply of 220 V at 300 rad/s angular…JEE Main 2021 (25 Feb, Shift 2)
A 750 Hz, 20 V (rms) source is connected to a resistance of 100 Ω, an inductance of…JEE Main 2020 (3 Sep, Shift 1)
In a series LR circuit, power of 400W is dissipated from a source of 250 V, 50 Hz. The…JEE Main 2020 (6 Sep, Shift 2)
A series AC circuit containing an inductor (20 mH), a capacitor (120 μ F) and a resistor…JEE Main 2019 (9 Jan, Shift 2)
An inductor 20 mH, a capacitor 100 μ F and a resistor 50 Ω are connected in series across…NEET 2018
In an a.c. circuit, the instantaneous e.m.f. and current are given by e = 100 sin 30 t i…JEE Main 2018