An RLC series circuit has L = 100 mH and C = 1 $\mu$F. It is connected to a 1000-Hz source emf is foundto lead the current by 75$\degree$. 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

The impedance of the circuit can be calculated using the formula:

$Z = \sqrt{R^2 + \left(X_L - X_Cight)^2}$

where $X_L$ and $X_C$ are the inductive and capacitive reactances, respectively. For an RLC series circuit, they are given by:

$X_L = 2\pi f L$ and $X_C = \frac{1}{2\pi f C}$

Substituting the given values, we get:

$X_L = 2\pi 	imes 1000 	imes 0.1 = 62.83 	ext{ }\Omega$

$X_C = \frac{1}{2\pi 	imes 1000 	imes 10^{-6}} = 159.15	ext{ }\Omega$

The phase angle between the voltage and current can be calculated using the formula:

$	heta = 	an^{-1}\left(\frac{X_L - X_C}{R}ight)$

Substituting the given value of 75°, we get:

$75 = 	an^{-1}\left(\frac{62.83 - 159.15}{R}ight)$

Solving for R, we get:

$R = \frac{X_L - X_C}{	an 75} = 126	ext{ }\Omega$

Therefore, the answer is B.

An RLC Series Circuit Has L = 100 MH and C