Advertisements
Advertisements
प्रश्न
The magnetic field at a point inside a 2.0 mH inductor-coil becomes 0.80 of its maximum value in 20 µs when the inductor is joined to a battery. Find the resistance of the circuit.
उत्तर
Given:-
Inductance of the inductor, L = 2.0 mH
Let the resistance in the circuit be R and the steady state value of the current be i0.
At time t , current i in the LR circuit is given by
i = i0(1 − e−t/τ)
Here,
\[\tau = \frac{L}{R}=\] Time constant
On multiplying both sides by µ0n, we get
n = Number of turns per unit length of the coil
µ0ni = µ0ni0(1 − e−t/τ)
⇒ B = B0(1 − e−tR/L)
⇒ 0.8 B0 = B0
\[\left( 1 - e^\frac{- 20 \times {10}^{- 6} R}{2 \times {10}^{- 3}} \right)\]
⇒ 0.8 = (1 − e−R/100)
⇒ e−R/100 = 0.2
⇒ ln (e−R/100) = ln (0.2)
`rArr -R/100=-1.693`
⇒ R = 169.3 Ω
APPEARS IN
संबंधित प्रश्न
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?
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.
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.
Derive an expression for the average power consumed in a series LCR circuit connected to a.c. source in which the phase difference between the voltage and the current in the circuit is Φ.
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.
In a series, LCR circuit, obtain an expression for the resonant frequency,
Answer the following question.
In a series LCR circuit connected across an ac source of variable frequency, obtain the expression for its impedance and draw a plot showing its variation with frequency of the ac source.
Figure shows a series LCR circuit connected to a variable frequency 230 V source. L = 5.0 H, C = 80 µF, R = 40 Ω.
- Determine the source frequency which drives the circuit in resonance.
- Obtain the impedance of the circuit and the amplitude of current at the resonating frequency.
- Determine the rms potential drops across the three elements of the circuit. Show that the potential drop across the LC combination is zero at the resonating frequency.
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 ______.
In an LCR circuit having L = 8 henery. C = 0.5 µF and R = 100 ohm in series, the resonance frequency in radian/sec is
Which of the following components of an LCR circuit, with a.c. supply, dissipates energy?
A series LCR circuit containing a 5.0 H inductor, 80 µF capacitors, and 40 Ω resistor is connected to a 230 V variable frequency ac source. The angular frequencies of the source at which power is transferred to the circuit are half the power at the resonant angular frequency are likely to be ______.
Define Impedance.
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
- the impedance of the circuit
- phase angle, and
- the voltage drop across the inductor.
Which of the following statements about a series LCR circuit connected to an ac source is correct?
When an alternating voltage of 220V is applied across device X, a current of 0.25A flows which lags behind the applied voltage in phase by π/2 radian. If the same voltage is applied across another device Y, the same current flows but now it is in phase with the applied voltage.
- Name the devices X and Y.
- 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.
Three students, X, Y and Z performed an experiment for studying the variation of a.c. 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.
- Who used minimum resistance?
- In which case will the quality Q factor be maximum?
- What did the students conclude about the nature of impedance at resonant frequency (f0)?
- An ideal capacitor is connected across 220V, 50Hz, and 220V, 100Hz supplies. Find the ratio of current flowing through it in the two cases.
