MHT CET · Physics · Alternating Current
Which one of the following graph represent correctly the variation of impedance (Z) of a series LCR circuit with the frequency ( \(v\) ) of applied a.c.?
- A A
- B B
- C C
- D D
Answer & Solution
Correct Answer
(B) B
Step-by-step Solution
Detailed explanation
\(Z=\sqrt{R^2+\left(2 \pi v L-\frac{1}{2 \pi \nu C}\right)^2}\)
From above equation at \(v=0 \Rightarrow Z=\infty\)
When \(v=\frac{1}{2 \pi \sqrt{\mathrm{LC}}}\) (resonant frequency).
\(\Rightarrow \mathrm{Z}=\mathrm{R}\)
For \(v \gt \frac{1}{2 \pi \sqrt{L C}} \Rightarrow Z\) starts increasing.
i.e., for frequency \(0-v_r, Z\) decreases and for \(v_r\) to \(\infty, \mathrm{Z}\) increases. This is justified by graph (B).
From above equation at \(v=0 \Rightarrow Z=\infty\)
When \(v=\frac{1}{2 \pi \sqrt{\mathrm{LC}}}\) (resonant frequency).
\(\Rightarrow \mathrm{Z}=\mathrm{R}\)
For \(v \gt \frac{1}{2 \pi \sqrt{L C}} \Rightarrow Z\) starts increasing.
i.e., for frequency \(0-v_r, Z\) decreases and for \(v_r\) to \(\infty, \mathrm{Z}\) increases. This is justified by graph (B).
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