For an L C R circuit driven at frequency ω, the equation reads L d i d t + R i + q C = v t = v m sin ω t Multiply the equation by i and simplify where possible.

L t d t d t + R t 2 + q t c = v t ; L t d t d t = d d t 1 2 L t 2 = rate of change of energy stored in an inductor. R i 2 = joule heating loss q C t = d d t q 2 2 C = rate of change of energy stored in the capacitor. v t = rate at which driving force pours in energy. It goes into (i) ohmic loss and (ii) increase of stored energy. ∫ 0 T d t d d t 1 2 t 2 + q 2 C + ∫ 0 T R t 2 d t = ∫ 0 T v t d t 0 + + v e = ∫ 0 T v t d t ∫ 0 T v t d t > 0 if phase difference, a constant is acute.

For an L C R circuit driven at frequency ω, the equation reads L d i d t + R i + q C = v t = v m sin ω t Interpret each term physically.

L t d t d t + R t 2 + q t c = v t ; L t d t d t = d d t 1 2 L t 2 = rate of change of energy stored in an inductor. R i 2 = joule heating loss q C t = d d t q 2 2 C = rate of change of energy stored in the capacitor. v t = rate at which driving force pours in energy. It goes into (i) ohmic loss and (ii) increase of stored energy. ∫ 0 T d t d d t 1 2 t 2 + q 2 C + ∫ 0 T R t 2 d t = ∫ 0 T v t d t 0 + + v e = ∫ 0 T v t d t ∫ 0 T v t d t > 0 if phase difference, a constant is acute.

For an L C R circuit driven at frequency ω, the equation reads L d i d t + R i + q C = v t = v m sin ω t Cast the equation in the form of a conservation of energy statement.

L t d t d t + R t 2 + q t c = v t ; L t d t d t = d d t 1 2 L t 2 = rate of change of energy stored in an inductor. R i 2 = joule heating loss q C t = d d t q 2 2 C = rate of change of energy stored in the capacitor. v t = rate at which driving force pours in energy. It goes into (i) ohmic loss and (ii) increase of stored energy. ∫ 0 T d t d d t 1 2 t 2 + q 2 C + ∫ 0 T R t 2 d t = ∫ 0 T v t d t 0 + + v e = ∫ 0 T v t d t ∫ 0 T v t d t > 0 if phase difference, a constant is acute.

For an L C R circuit driven at frequency ω, the equation reads L d i d t + R i + q C = v t = v m sin ω t Intergrate the equation over one cycle to find that the phase difference between v and i must be acute.

L t d t d t + R t 2 + q t c = v t ; L t d t d t = d d t 1 2 L t 2 = rate of change of energy stored in an inductor. R i 2 = joule heating loss q C t = d d t q 2 2 C = rate of change of energy stored in the capacitor. v t = rate at which driving force pours in energy. It goes into (i) ohmic loss and (ii) increase of stored energy. ∫ 0 T d t d d t 1 2 t 2 + q 2 C + ∫ 0 T R t 2 d t = ∫ 0 T v t d t 0 + + v e = ∫ 0 T v t d t ∫ 0 T v t d t > 0 if phase difference, a constant is acute.

E M B I B E

NCERT Exemplar Physics - Class 12>Chapter 7 - Alternating Current>LA

NCERT Solutions for Chapter: Alternating Current, Exercise 4: LA

Author:NCERT

NCERT Physics Solutions for Exercise - NCERT Solutions for Chapter: Alternating Current, Exercise 4: LA

Attempt the practice questions on Chapter 7: Alternating Current, Exercise 4: LA with hints and solutions to strengthen your understanding. NCERT Exemplar Physics - Class 12 solutions are prepared by Experienced Embibe Experts.

Questions from NCERT Solutions for Chapter: Alternating Current, Exercise 4: LA with Hints & Solutions

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12th CBSE

IMPORTANT

NCERT Exemplar Physics - Class 12>Chapter 7 - Alternating Current>LA>Q 7.29

Consider the $L C R$ circuit shown in Fig 7.6. Find the net current $i$ and the phase of $i$ . Show that $i = \frac{v}{Z}$ .
Find the impedence $Z$ for this circuit.