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महाराष्ट्र राज्य शिक्षण मंडळएचएससी विज्ञान (सामान्य) इयत्ता १२ वी

Define Impedance.

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प्रश्न

Define Impedance.

व्याख्या
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उत्तर

The effective opposition offered by the inductor, capacitor and resistor connected in series to flow of AC current. is called impedance.

Z = `sqrt("R"^2 + (Χ_"L" - Χ_"C")^2)`

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2021-2022 (March) Set 1

संबंधित प्रश्‍न

In a series LCR circuit, VL = VC ≠ VR. What is the value of power factor?


A series LCR circuit is connected across an a.c. source of variable angular frequency 'ω'. Plot a graph showing variation of current 'i' as a function of 'ω' for two resistances R1 and R2 (R1 > R2).

Answer the following questions using this graph :

(a) In which case is the resonance sharper and why?

(b) In which case in the power dissipation more and why?


A voltage V = V0 sin ωt is applied to a series LCR circuit. Derive the expression for the average power dissipated over a cycle. Under what condition (i) no power is dissipated even though the current flows through the circuit, (ii) maximum power is dissipated in the circuit?


Why does current in a steady state not flow in a capacitor connected across a battery? However momentary current does flow during charging or discharging of the capacitor. Explain. 


In a series LCR circuit, obtain the condition under which the impedance of the circuit is minimum ?


The figure shows a series LCR circuit with L = 10.0 H, C = 40 μF, R = 60 Ω connected to a variable frequency 240 V source, calculate

(i) the angular frequency of the source which drives the circuit at resonance,

(ii) the current at the resonating frequency,

(iii) the rms potential drop across the inductor at resonance.


Find the value of t/τ for which the current in an LR circuit builds up to (a) 90%, (b) 99% and (c) 99.9% of the steady-state value.


An LR circuit having a time constant of 50 ms is connected with an ideal battery of emf ε. find the time elapsed before (a) the current reaches half its maximum value, (b) the power dissipated in heat reaches half its maximum value and (c) the magnetic field energy stored in the circuit reaches half its maximum value.


An LR circuit with emf ε is connected at t = 0. (a) Find the charge Q which flows through the battery during 0 to t. (b) Calculate the work done by the battery during this period. (c) Find the heat developed during this period. (d) Find the magnetic field energy stored in the circuit at time t. (e) Verify that the results in the three parts above are consistent with energy conservation.


Draw a labelled graph showing a variation of impedance of a series LCR circuit with frequency of the a.c. supply.


Answer the following question.
Draw the diagram of a device that is used to decrease high ac voltage into a low ac voltage and state its working principle. Write four sources of energy loss in this device.  


Derive an expression for the average power dissipated in a series LCR circuit.


Keeping the source frequency equal to the resonating frequency of the series LCR circuit, if the three elements, L, C and R are arranged in parallel, show that the total current in the parallel LCR circuit is minimum at this frequency. Obtain the current rms value in each branch of the circuit for the elements and source specified for this frequency.


Obtain the resonant frequency and Q-factor of a series LCR circuit with L = 3.0 H, C = 27 µF, and R = 7.4 Ω. It is desired to improve the sharpness of the resonance of the circuit by reducing its ‘full width at half maximum’ by a factor of 2. Suggest a suitable way.


In a series LCR circuit supplied with AC, ______.


In LCR circuit if resistance increases quality factor ______.

In series combination of R, L and C with an A.C. source at resonance, if R = 20 ohm, then impedence Z of the combination is ______.


In an LCR series a.c. circuit, the voltage across each of the components, L, C and R is 50V. The voltage across the LC combination will be ______.


A coil of 40 henry inductance is connected in series with a resistance of 8 ohm and the combination is joined to the terminals of a 2 volt battery. The time constant of the circuit is ______.


To reduce the resonant frequency in an LCR series circuit with a generator


A series LCR circuit containing 5.0 H inductor, 80 µF capacitor and 40 Ω resistor is connected to 230 V variable frequency ac source. The angular frequencies of the source at which power transferred to the circuit is half the power at the resonant angular frequency are likely to be ______.


Which of the following combinations should be selected for better tuning of an LCR circuit used for communication?


A series RL circuit with R = 10 Ω and L = `(100/pi)` mH is connected to an ac source of voltage V = 141 sin (100 πt), where V is in volts and t is in seconds. Calculate

  1. the impedance of the circuit
  2. phase angle, and
  3. the voltage drop across the inductor.

An alternating voltage of 220 V is applied across a device X. A current of 0.22 A flows in the circuit and it lags behind the applied voltage in phase by π/2 radian. When the same voltage is applied across another device Y, the current in the circuit remains the same and it is in phase with the applied voltage.

  1. Name the devices X and Y and,
  2. Calculate the current flowing in the circuit when the same voltage is applied across the series combination of X and Y.

A series LCR circuit is connected to an ac source. Using the phasor diagram, derive the expression for the impedance of the circuit.


Select the most appropriate option with regard to resonance in a series LCR circuit.


Three students, X, Y and Z performed an experiment for studying the variation of ac with frequency in a series LCR circuit and obtained the graphs as shown below. They all used

  • an AC source of the same emf and
  • inductance of the same value.

  1. Who used minimum resistance?
  2. In which case will the quality Q factor be maximum?
  3. What did the students conclude about the nature of impedance at resonant frequency (f0)?
  4. An ideal capacitor is connected across 220 V, 50 Hz, and 220 V, 100 Hz supplies. Find the ratio of current flowing through it in the two cases.

A series LCR circuit (L = 10 H, C = 10 µF, R = 50 Ω) is connected to V = 200 sin⁡ (100t). If ν0​ is the resonant frequency and ν is the source frequency, then ______.


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