Advertisements
Advertisements
प्रश्न
A series LCR circuit is connected to an ac source. Using the phasor diagram, derive the expression for the impedance of the circuit.
Advertisements
उत्तर
 LCR Circuit |
 |
E = E0 sinωt is applied to a series LCR circuit. Since all three of them are connected in series the current through them is the same. But the voltage across each element has a different phase relation with the current.
The potential difference VL, VC and VR across L, C and R at any instant is given by VL = IXL, VC = IXC and VR = IR, where I is the current at that instant.
VR is in phase with I. VL leads I by 90° and VC lags behind I by 90° so the phasor diagram will be as shown Assuming VL > VC, the applied emf E which is equal to the resultant of the potential drop across R, L & C is given as
`E^2 = I^2[R^2 + (X_L - X_C)^2]`
Or I = `E/sqrt[[R^2 + (X_L - X_C)^2]` = `E/Z`, Where Z is Impedance.
Emf leads current by a phase angle φ as `tanφ = (V_L - V_C)/R = (X_L - X_C)/R`
APPEARS IN
संबंधित प्रश्न
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.
An L-R circuit has L = 1.0 H and R = 20 Ω. It is connected across an emf of 2.0 V at t = 0. Find di/dt at (a) t = 100 ms, (b) t = 200 ms and (c) t = 1.0 s.
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.
An inductor of inductance 2.00 H is joined in series with a resistor of resistance 200 Ω and a battery of emf 2.00 V. At t = 10 ms, find (a) the current in the circuit, (b) the power delivered by the battery, (c) the power dissipated in heating the resistor and (d) the rate at which energy is being stored in magnetic field.
The current in a discharging LR circuit without the battery drops from 2.0 A to 1.0 A in 0.10 s. (a) Find the time constant of the circuit. (b) If the inductance of the circuit 4.0 H, what is its resistance?
(i) An a.c. source of emf ε = 200 sin omegat is connected to a resistor of 50 Ω . calculate :
(1) Average current (`"I"_("avg")`)
(2) Root mean square (rms) value of emf
(ii) State any two characteristics of resonance in an LCR series circuit.
An ac circuit as shown in the figure has an inductor of inductance L and a resistor or resistance R connected in series. Using the phasor diagram, explain why the voltage in the circuit will lead the current in phase.
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.
Draw the impedance triangle for a series LCR AC circuit and write the expressions for the impedance and the phase difference between the emf and the current.
To an ac power supply of 220 V at 50 Hz, a resistor of 20 Ω, a capacitor of reactance 25 Ω and an inductor of reactance 45 Ω are connected in series. The corresponding current in the circuit and the phase angle between the current and the voltage is respectively:
