In a circuit,L,C,and R are connected in serie | vedclass

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

Question

(A) In an $LCR$ series circuit,the phase difference $\phi$ between voltage and current is given by $	an \phi = \frac{X_C - X_L}{R}$.Since the current

Vedclass · Accepted Answer

$\frac{1}{2 \pi f(2 \pi f L+R)}$

Vedclass · Answer

(A) In an $LCR$ series circuit,the phase difference $\phi$ between voltage and current is given by $	an \phi = \frac{X_C - X_L}{R}$.Since the current leads the voltage,the phase angle is $\phi = -45^{\circ}$.Therefore,$	an(-45^{\circ}) = \frac{X_C - X_L}{R} = -1$.This implies $X_L - X_C = R$,or $X_C - X_L = -R$.However,the standard convention for current leading is $	an \phi = \frac{X_L - X_C}{R}$ where $\phi$ is the phase of voltage relative to current. If current leads,$\phi = -45^{\circ}$,so $	an(-45^{\circ}) = -1 = \frac{X_L - X_C}{R}$,which gives $X_C - X_L = R$.Substituting $X_C = \frac{1}{2 \pi f C}$ and $X_L = 2 \pi f L$:$\frac{1}{2 \pi f C} - 2 \pi f L = R$$\frac{1}{2 \pi f C} = R + 2 \pi f L$$C = \frac{1}{2 \pi f (R + 2 \pi f L)}$.

In a circuit,$L$,$C$,and $R$ are connected in series with an alternating voltage source of frequency $f$. When the current in the circuit leads the voltage by $45^{\circ}$,the value of $C$ is

Similar Questions

Consider the $L-C-R$ circuit given below. The circuit is driven by a $50 \,Hz, AC$ source with peak voltage $220 \,V$. If $R=400 \,\Omega, C=200 \,\mu F$ and $L=6 \,H$,the maximum current in the circuit is closest to ............ $A$.

The figure shows a combination of inductances and capacitances. The resonant frequency of the $L-C$ circuit is:

In an $LCR$ series circuit, the potential difference across the terminals of the inductor, capacitor and resistor is $60 \text{ V}$, $30 \text{ V}$ and $40 \text{ V}$ respectively. Then the supply voltage will be equal to (in $\text{ V}$)

In an $R-L-C$ series circuit, the potential difference across each element is $20 \, V$. If the value of the resistance $R$ is doubled, what will be the potential difference across $R, L$, and $C$ respectively?

Vedclass Test Series

Exam Paper Generator

Online Exam Module