Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa

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

Option: 1

3


Option: 2

-


Option: 3

-


Option: 4

-


Answers (1)

best_answer

\mathrm{p=50w}

\mathrm{c=\frac{50}{\pi \sqrt{x}}}

\mathrm{V_{rms}=200}

\mathrm{f=50Hz}

\mathrm{\text current\: through\: lamp=I}

                                           \mathrm{=\frac{p}{v}}

                                            \mathrm{=\frac{1}{2}A}

\mathrm{I=\frac{V_{rms}}{z}}

\mathrm{\frac{1}{2}=\frac{200}{\sqrt{x_{c}^{2}+R^{2}}}}

\mathrm{{\sqrt{x_{c}^{2}+R^{2}}=400}}

\mathrm{X^{2}_{c}+\left [ \frac{\left ( 100 \right )^{2}}{50} \right ]^{2}=160000}

\mathrm{X^{2}_{c}+40000=160000}

\mathrm{X^{2}_{c}=\frac{1}{\left ( \frac{2\pi \times 50\times 50\times 10^{-6}}{\pi \sqrt{x}} \right )^{2}}=120000}

\mathrm{\frac{x}{25\times 10^{6}\times 10^{-12}}=120000}

\mathrm{x=25\times 12\times 10^{-2}}

\mathrm{x=3}

Posted by

shivangi.shekhar

View full answer

JEE Main high-scoring chapters and topics

Study 40% syllabus and score up to 100% marks in JEE

Similar Questions

Trending Articles/News

anam-khan

JEE Main 2025: BTech CSE cut-offs for PwD candidates at NITs make entry easy; top institutes still selective
anam-khan

73 or 99 percentile? JEE Main result questioned, J-K candidate says, ‘Don’t create hype’
anam-khan

JEE Main 2025: 11 from Kota coaching centres among 24 students with 100 percentile

Latest Question