Question

A 100volt ac source of angular frequency 500rad/sec is connected to lcr circuit with l=0.8hz,c =5uf,r=10ohm all connected in series.Potential differnce across resistance is

Answer 1

Answer:

The Potential difference across resistance is 99.66 volt.

Explanation:

Given that,

Voltage = 100 volt

Frequency = 500 rad/sec

Inductance = 0.8 millihenry

Capacitance = 5μf

Resistance = 10 ohm

We need to calculate the $X_{L}$

Using formula of $X_{L}$

$X_{L}=2\pi f L$

Put the value into the formula

$X_{L}=2\times\pi\times500\times0.8\times10^{-3}$

$X_{L}=2.51\ ohm$

We need to calculate the $X_{C}$

Using formula of $X_{C}$

$X_{C}=\dfrac{1}{2\pi f C}$

Put the value into the formula

$X_{C}=\dfrac{1}{2\pi\times500\times5\times10^{-6}}$

$X_{C}=63.6\ \Omega$

We need to calculate the impedance

Using formula of impedance

$Z=\sqrt{R^2+(X_{L}-X_{C})^2}$

$Z=\sqrt{(10)^2+(2.51-63.6)^2}$

$Z=61.90\ ohm$

We need to calculate the rms value of current

Using formula of rms current

$I_{rms}=\dfrac{V}{R}$

$I_{rms}=\dfrac{100}{61.90}$

$I_{rms}=1.61\ A$

We need to calculate the Potential difference across resistance

Using formula of potential difference

$V = I\times R$

Put the value into the formula

$V = 1.61\times61.90$

$V =99.66\ Volt$

Hence, The Potential difference across resistance is 99.66 volt.