Advertisements
Advertisements
प्रश्न
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.
Advertisements
उत्तर
Given:
R = 10 Ω
L = `(100/pi)` mH
V = 141 sin (100 π)t
From this equation, we get the value of ω = 100π and V = 141 volt
- To find: Impedance (Z)
Z = `sqrt(R^2 + X_L^2)`
Where Z is the impedance, R is the resistance, and XL is the impedance,
XL = ωL
XL = `(100pi xx 100)/(pi xx 10^-3)`
XL = 10Ω
Z = `sqrt(R^2 + X_L^2)`
Z = `sqrt((10)^2 + (10)^2)`
Z = `sqrt200`
Z = `10sqrt2`Ω - Phase Angle (Φ):
We can calculate the phase angle by the following formula,
`cosphi = R/Z`
`cosphi = 10/(10sqrt2)`
`cosphi = 1/sqrt2`
`phi = 45^circ` - Voltage drop:
`V_L = IX_L`
= `V/Z xx X_L`
`V_L = 141/(10sqrt2) xx 10`
`V_L = 141/sqrt2`
`V_L ≅ 100` volt
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?
If an LCR series circuit is connected to an ac source, then at resonance the voltage across ______.
At resonance frequency the impedance in series LCR circuit is ______.
The resonant frequency of a RF oscillator is 1 MHz and its bandwidth is 10 kHz. The quality factor will be :
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 ______.
For an LCR circuit driven at frequency ω, the equation reads
`L (di)/(dt) + Ri + q/C = v_i = v_m` sin ωt
- Multiply the equation by i and simplify where possible.
- Interpret each term physically.
- Cast the equation in the form of a conservation of energy statement.
- Integrate the equation over one cycle to find that the phase difference between v and i must be acute.
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:
In the given circuit, rms value of current (Irms) through the resistor R is:
When a capacitor is connected in series LR circuit, the alternating current flowing in the circuit ______
Out of the following which one is NOT the characteristic of LCR series resonant circuit?
