A series combination of resistor R and capaci | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) The impedance of an $RC$ series circuit is given by $Z = \sqrt{R^2 + X_C^2}$, where $X_C = 1/(\omega C)$.Initial current $I_1 = V / \sqrt{R^2 + X_

Vedclass · Accepted Answer

$\sqrt{0.6}$

Vedclass · Answer

(D) The impedance of an $RC$ series circuit is given by $Z = \sqrt{R^2 + X_C^2}$, where $X_C = 1/(\omega C)$.Initial current $I_1 = V / \sqrt{R^2 + X_C^2}$.When frequency changes to $\omega' = \omega/3$, the new capacitive reactance becomes $X_C' = 1/((\omega/3)C) = 3X_C$.The new current is $I_2 = V / \sqrt{R^2 + (3X_C)^2}$.Given $I_2 = I_1/2$, so $2I_2 = I_1$.Substituting the expressions: $2V / \sqrt{R^2 + 9X_C^2} = V / \sqrt{R^2 + X_C^2}$.Squaring both sides: $4 / (R^2 + 9X_C^2) = 1 / (R^2 + X_C^2)$.$4(R^2 + X_C^2) = R^2 + 9X_C^2$.$4R^2 + 4X_C^2 = R^2 + 9X_C^2$.$3R^2 = 5X_C^2$.$X_C^2 / R^2 = 3/5 = 0.6$.Therefore, the ratio $X_C / R = \sqrt{0.6}$.

$A$ series combination of resistor $R$ and capacitor $C$ is connected to an a.c. source of angular frequency $\omega$. Keeping the voltage same, if the frequency is changed to $\omega/3$, the current becomes half of the original current. Then the ratio of capacitive reactance and resistance is

Similar Questions

In an $AC$ circuit,a resistance of $R \, \Omega$ is connected in series with an inductance $L$. If the phase angle between voltage and current is $45^o$,the value of inductive reactance will be:

When a coil is connected to an $AC$ supply of frequency $50 \, Hz$, a current of $4 \, A$ flows in it and it consumes $240 \, W$ power. If the potential difference across the coil is $100 \, V$, then the inductance value of the coil is

In the $AC$ circuit shown,$E = E_0 \sin(\omega t + \phi)$ and $i = i_0 \sin(\omega t + \phi + \frac{\pi}{4})$. Then,the box contains:

In the given figure,the current amplitude is

In an $RL$ circuit,the resistance is $\pi \sqrt{3} \,\Omega$. The phase difference between the current and the voltage is $30^\circ$. The $ac$ frequency is $50 \,Hz$. The inductance is . . . . . . $Henry$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module