9. the total impedance in this circuit is
a 970 ω
b 703 ω
c 502 ω
d 241 ω

Question

9. the total impedance in this circuit is
 a 970 ω
 b 703 ω
 c 502 ω
 d 241 ω

Accepted Answer

# Explanation:
## Step1: Calculate inductive reactance $X_L$
The formula for inductive reactance is $X_L = 2\pi fL$.
Given $f = 23\times10^{3}\text{ Hz}$ and $L=2.1\times 10^{- 3}\text{ H}$.
$$
\begin{align*}
X_L&=2\pi\times(23\times 10^{3})\times(2.1\times 10^{-3})\
&=2\pi\times23\times2.1\
&\approx 304.5\Omega
\end{align*}
$$
## Step2: Calculate total impedance $Z$ for parallel $RL$ circuit
For a parallel $RL$ circuit, the formula for impedance $Z=\frac{R\times X_L}{\sqrt{R^{2}+X_L^{2}}}$. Here $R = 400\Omega$ and $X_L\approx304.5\Omega$
$$
\begin{align*}
Z&=\frac{400\times304.5}{\sqrt{400^{2}+304.5^{2}}}\
&=\frac{121800}{\sqrt{160000 + 92720.25}}\
&=\frac{121800}{\sqrt{252720.25}}\
&=\frac{121800}{502.71}\
&\approx502\Omega
\end{align*}
$$

# Answer:
C. $502\ \Omega$

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QUESTION IMAGE

Question

Explanation:

Step1: Calculate inductive reactance \(X_L\)

Step2: Calculate total impedance \(Z\) for parallel \(RL\) circuit

Answer: