Skip to content

Find the condition for… (Class 12 Physics 2023, Q27b)

questionbuddy.in/q/cbse-12-physics-2023-55-1-1-q27b-condition-resonance-series-lcr-circuit

PhysicsCBSE Class 12 · Board exam 2023, set 55/1/1 · 3 marks · Short answer

CBSE Class 12 Physics 2023: question 27(b)

Set in the CBSE Class 12 board exam of 2023, paper 55/1/1, section C, question 27(b), for 3 marks. Try it first; the hints and our step-by-step solution are below.

Q27(b) · 3 marks · Short answerAlternating Current

Find the condition for resonance in a series LCR circuit connected to a source , where can be varied. Give the factors on which the resonant frequency of a series LCR circuit depends. Plot a graph showing the variation of electric current with frequency in a series LCR circuit.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2023 board paper, set 55/1/1.

Hints

Open one hint at a time and try again before the next.

Hint 1

When is the impedance smallest?

Hint 2

Set the inductive and capacitive reactances equal and solve for .

Step-by-step solution

Each step shows the marks it earns, as an examiner would award them. Checked by an independent re-solve from the question paper.

  1. with . Current is maximum when Z is minimum, i.e. when : . This is the condition for resonance (then ).

    1 mark

  2. Resonant frequency depends only on the inductance L and capacitance C (not on R).

    1 mark

  3. Graph (described): current amplitude on y-axis vs angular frequency on x-axis; current rises from a small value, reaches a sharp peak at and then decreases. For smaller R the peak is higher and sharper; for larger R it is lower and flatter.

    1 mark

Answer: Resonance when , ; depends on L and C; current peaks at .

Where the marks are

  • Condition , (1 mark)
  • Resonant frequency depends on L and C (1 mark)
  • Graph of current vs frequency with peak at (1 mark)

Revise the chapter

Practise this chapterBoard-style questions from Alternating Current, one at a time, marked against the answer key and marking points.Back to the full paper2023 board paper, set 55/1/1: every question, by section.

The question is transcribed from the official paper; figures are described in words. The solution, hints and chapter tag are ours. Spotted an error? Write tosupport@questionbuddy.in.