In the given circuit, the magnitude of $\mathrm{V}_{\mathrm{L}}$ and $\mathrm{V}_{\mathrm{C}}$ are twice that of $\mathrm{V}_{\mathrm{R}}$. Given that $\mathrm{f}=50 \mathrm{~Hz}$, the inductance of the coil is $\frac{1}{\mathrm{~K} \pi} \mathrm{mH}$. The value of K is

JEE Main · 2022 · 28 Jun 2022 · Shift 2 · Alternating Current

In the given circuit, the magnitude of

V_{L}

and

V_{C}

are twice that of

V_{R}

. Given that

f = 50 Hz

, the inductance of the coil is

\frac{1}{K π} mH

. The value of K is

Answer: 0

Because

V_{L} = V_{C} = 2 V_{R}

, the corresponding reactances satisfy

X_{L} = X_{C} = 2 R

. With the circuit resistance

R = 5 Ω

this makes

X_{L} = 10 Ω

. From

X_{L} = ω L = 2 π f L

with

f = 50

Hz,

L = \frac{X _{L}}{2 π f} = \frac{10}{100 π} = \frac{1}{10 π} H = \frac{100}{π} mH

. Comparing with the stated form

L = \frac{1}{K π}

mH gives

\frac{1}{K} = 100

, so

K = 0.01

, which the integer answer key records as

0

JEE Main · 2022 · 28 Jun 2022 · Shift 2 · Integer answer