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Problems in General Physics

PART THREE. ELECTRODYNAMICS

Q.146. A capacitor with capacitance C and a coil with active r

Problems in General Physics

Class 11

IE Irodov

Chapter 1: PART ONE. PHYSICAL FUNDAMENTALS OF MECHANICS

277 questions

Chapter 2: PART TWO. THERMODYNAMICS AND MOLECULAR PHYSICS

9 questions

Chapter 3: PART THREE. ELECTRODYNAMICS

46 questions

Q.145. A capacitor with capacitance C = 1.0 μF and a coil with active resistance R = 0.10Ω and inductance L = 1.0 mH are connected in parallel to a source of sinusoidal voltage V = 31 V. Find:
(a) the frequency ω at which the resonance sets in;
(b) the effective value of the fed current in resonance, as well as the corresponding currents flowing through the coil and through the capacitor.

Q.146. A capacitor with capacitance C and a coil with active resistance R and inductance L are connected in parallel to a source of sinusoidal voltage of frequency ω. Find the phase difference between the current fed to the circuit and the source voltage.

Q.147. An atom in the state with quantum numbers L = 2, S = 1. is located in a weak magnetic field. Find its magnetic moment if the least possible angle between the angular momentum and the field direction is known to be equal to 30°.

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Chapter 4: PART FOUR. OSCILLATIONS AND WAVES

155 questions

Chapter 5: PART FIVE. OPTICS

215 questions

Chapter 6: PART SIX. ATOMIC AND NUCLEAR PHYSICS

271 questions

Question

Hard

Solving time: 5 mins

Q.146. A capacitor with capacitance C and a coil with active resistance R and inductance L are connected in parallel to a source of sinusoidal voltage of frequency ω. Find the phase difference between the current fed to the circuit and the source voltage.

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Text solutionVerified

We use the method of complex voltage

V = V_{0} e^{iω t}

Then

I_{C} = \frac{V _{0} e ^{iω t}}{\frac{1}{iω C}} = iω C V_{0} e^{iω t}

I_{L, R} = \frac{V _{0} e ^{iω t}}{R + iω L}

I = I_{C} + I_{L, R} = V_{0} \frac{R - iω L + iω C ( R ^{2} + ω ^{2} L ^{2} )}{R ^{2} + ω ^{2} L ^{2}} e^{iωi}

Then taking the real part

I = \frac{V _{0} R ^{2} + { ω C ( R ^{2} + ω ^{2} L ^{2} ) - ω L } ^{2}}{R ^{2} + ω ^{2} L ^{2}} cos (ω t - φ)

where

tan φ = \frac{ω L - ω C ( R ^{2} + ω ^{2} L ^{2} )}{R}

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Question Text	Q.146. A capacitor with capacitance C and a coil with active resistance R and inductance L are connected in parallel to a source of sinusoidal voltage of frequency ω. Find the phase difference between the current fed to the circuit and the source voltage.
Topic	Alternating Current
Subject	Physics
Class	Class 12
Answer Type	Text solution:1
Upvotes	71

Q.146. A capacitor with capacitance C and a coil with active resistance R and inductance L are connected in parallel to a source of sinusoidal voltage of frequency ω. Find the phase difference between the current fed to the circuit and the source voltage.

Text solutionVerified

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Q.146. A capacitor with capacitance C and a coil with active resistance R and inductance L are connected in parallel to a source of sinusoidal voltage of frequency ω. Find the phase difference between the current fed to the circuit and the source voltage.

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