KCET · Physics · Alternating Current
In the series \(L-C-R\) circuit shown, the impedance is
- A \(200 \Omega\)
- B \(100 \Omega\)
- C \(300 \Omega\)
- D \(500 \Omega\)
Answer & Solution
Correct Answer
(D) \(500 \Omega\)
Step-by-step Solution
Detailed explanation
\(X_{L} =2 \pi f L \)
\( =2 \pi\left(\frac{50}{\pi}\right) \times 1=100 \Omega \)
\( X_{C} =\frac{1}{2 \pi f C}=\frac{1}{2 \pi\left(\frac{50}{\pi}\right) 20 \times 10^{-6}}=500 \Omega \)
\( \text {Impedance, } Z =\sqrt{R^{2}+\left(X_{C}-X_{L}\right)^{2}} \)
\( Z =\sqrt{(300)^{2}-(400)^{2}}=500 \Omega\)
\( =2 \pi\left(\frac{50}{\pi}\right) \times 1=100 \Omega \)
\( X_{C} =\frac{1}{2 \pi f C}=\frac{1}{2 \pi\left(\frac{50}{\pi}\right) 20 \times 10^{-6}}=500 \Omega \)
\( \text {Impedance, } Z =\sqrt{R^{2}+\left(X_{C}-X_{L}\right)^{2}} \)
\( Z =\sqrt{(300)^{2}-(400)^{2}}=500 \Omega\)
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