An RLC series circuit has L = 100 mH and C = 1 $\Omega$F.It is connected to a 1000-Hz source emf, and the voltage is found to lead the current by 75 ° .The value of R is:
A)12.6 $\Omega$
B)126 $\Omega$
C)175$\Omega$
D)1750 $\Omega$
E)1810 $\Omega$

Question

Quizplus · Accepted Answer

We can use the formula for the impedance of an RLC series circuit:

$Z_{total}=\sqrt{R^2+(X_L-X_C)^2}$

where $X_L$ is the inductive reactance and $X_C$ is the capacitive reactance.

We can also use the fact that the voltage leads the current by 75 degrees to determine the phase angle:

$	an{	heta}=\frac{X_L-X_C}{R}$

Given that $L=100 mH$, $C=1\mu F$, and $f=1000 Hz$, we can calculate the reactances:

$X_L=2\pi f L=62.8\Omega$

$X_C=\frac{1}{2\pi f C}=159.2\Omega$

Substituting these values into the formula for the impedance and the formula for the phase angle, we get:

$	an{(75^\circ)}=\frac{62.8-159.2}{R}=-1.936$

Solving for R, we get:

$R=\frac{96.4}{	an{(75^\circ)}}\approx126\Omega$

Therefore, the correct answer is B.

An RLC Series Circuit Has L = 100 MH and C