Question

a circuit with a 15 ω resistor, a 1.45 h inductor, and a frequency of 33 hz has a q of approximately ____. 20 148 1,500 300

Explanation:

Step1: Recall the formula for Q-factor in an RL circuit

The Q - factor (quality factor) of an RL circuit is given by the formula $Q=\frac{X_{L}}{R}$, where $X_{L}$ is the inductive reactance and $R$ is the resistance. The formula for inductive reactance is $X_{L} = 2\pi fL$, where $f$ is the frequency and $L$ is the inductance.

Step2: Calculate the inductive reactance $X_{L}$

Given $f = 33\space Hz$, $L=1.45\space H$.
Substitute into the formula $X_{L}=2\pi fL$:
$X_{L}=2\times\pi\times33\times1.45$
First, calculate $2\times33\times1.45 = 66\times1.45=95.7$
Then, $X_{L}=95.7\times\pi\approx95.7\times3.1416\approx300.6\space\Omega$ (approximate value of $\pi$ as 3.1416)

Step3: Calculate the Q - factor

We know that $R = 15\space\Omega$ and we just calculated $X_{L}\approx300.6\space\Omega$
Using the formula $Q=\frac{X_{L}}{R}$:
$Q=\frac{300.6}{15}\approx20.04$

Answer:

20