State any two characteristics of resonance in an L C R series circuit.

(i) In resonance, the X L = X c i.e. ωL = 1 / ωC (ii) The power factor of resonant circuit is 1. (iii)The frequency of applied voltage is equal to natural frequency of circuit. Also, the impedance of the circuit is minimum and the current in the circuit is maximum.

Draw a labelled graph showing the variation of inductive reactance X L verses frequency f .

Graph for inductive reactance ( X L ) with respect to frequency ( f ). We use relation between Inductive reactance and frequency, X L = ωL = 2 πfL . Here graph is straight line due to inductive reactance is directly proportional to its frequency.

An ac generator generating an emf of ε = 300 sin ( 100 π t ) V is connected to a series combination of 16 μ F capacitor, 1 H inductor and 100 Ω resistor. Calculate the power factor at resonant frequency.

Given in the series LCR circuit, emf ε = 300 sin ( 100 πt ) V , C = 16 μ F , L = 1 H , R = 100 Ω , ω = 100 π rad / s Power factor is cos θ θ = tan - 1 X L - X C R At resonance, X L = X C So, θ = 0 ∘ Power factor C o s 0 ∘ = 1

An ac generator generating an emf of ε = 300 sin ( 100 π t ) V is connected to a series combination of 16 μ F capacitor, 1 H inductor and 100 Ω resistor. Calculate the Resonant frequency.

Given in the series LCR circuit, emf ε = 300 sin ( 100 πt ) V , C = 16 μ F , L = 1 H , R = 100 Ω , ω = 100 π rad / s Resonant frequency is given by f ∘ = 1 2 π LC On putting values we get : f ∘ = 1 2 × 3 . 14 1 × 16 × 10 - 6 = 39 . 18 H z

An ac generator generating an emf of ε = 300 sin ( 100 π t ) V is connected to a series combination of 16 μ F capacitor, 1 H inductor and 100 Ω resistor. Calculate Impedance of the circuit at the given frequency.

Given in the series LCR circuit, emf ε = 300 sin ( 100 πt ) V , C = 16 μ F , L = 1 H , R = 100 Ω , ω = 100 π rad / s The impedance of the circuit is Z = R 2 + X L - X C 2 On putting the correct values in the equation we get : X L = ω L = 314 Ω X C = 1 ω C = 199 Ω Z = 57 Ω

E M B I B E

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR PHYSICS>Chapter 12 - Alternating Current>ICSE-2020>Q 15

MEDIUM

12th ICSE

IMPORTANT

Earn 100

Draw a labelled graph showing the variation of impedance $(Z)$ of a series LCR circuit versus frequency $(f)$ of an ac supply.

Important Questions on Alternating Current

EASY

12th ICSE

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR PHYSICS>Chapter 12 - Alternating Current>ICSE-2020>Q 16

When an alternating emf $e = 310 \sin (100 π t) V$ is applied to a series $L C R$ circuit, the current flowing through it is $i = 5 \sin (100 π t + π / 3) A$ . What is the phase difference between the current and the emf?

MEDIUM

12th ICSE

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR PHYSICS>Chapter 12 - Alternating Current>ICSE-2020>Q 17

When an alternating emf $e = 310 \sin (100 π t) V$ is applied to a series $L C R$ circuit, the current flowing through it is $i = 5 \sin (100 π t + π / 3) A$ . Calculate the average power consumed by the circuit.