Advertisements
Advertisements
प्रश्न
A device Y is connected across an AC source of emf e = e0 sin ωt. The current through Y is given as i = i0 sin (ωt + π/2).
- Identify the device Y and write the expression for its reactance.
- Draw graphs showing a variation of emf and current with time over one cycle of AC for Y.
- How does the reactance of the device Y vary with the frequency of the AC? Show graphically.
- Draw the phasor diagram for device Y.
Advertisements
उत्तर
1. The device Y is a capacitor. Its reactance is `"X"_"C" = 1/(omega"C")`, where ω is the angular frequency of the applied emf and C is the capacitance of the capacitor.
2.
3. `"X"_"C" = 1/(omega"C") = 1/(2pi"fC")`. Thus `"X"_"C" prop 1/"f"`, where f is the frequency of AC.
Suppose C = `(1000/(2pi))`pF
For f = 100 Hz, XC = 1 × 107 Ω = 10 M Ω;
for f = 200 Hz, XC = 5 M Ω;
for f = 300 Hz, XC = `10/3` M Ω;
for f = 400 Hz, XC = 2.5 M Ω
for f = 500 Hz, XC = 2 M Ω and so on.
(1 M Ω = 106 Ω)
Variation of `1/(omega"C")` with f
4. Phasor diagram for a purely capacitive circuit
The phasor representing the peak emf (e0) makes an angle wt in an anticlockwise direction with respect to the horizontal axis. As the current leads the voltage by 90°, the phasor representing the peak current (i0) is turned 90° anticlockwise with respect to the phasor representing emf e0. The projections of these phasors on the vertical axis give instantaneous values of e and i.
APPEARS IN
संबंधित प्रश्न
A 2 µF capacitor, 100 Ω resistor and 8 H inductor are connected in series with an AC source.
(i) What should be the frequency of the source such that current drawn in the circuit is maximum? What is this frequency called?
(ii) If the peak value of e.m.f. of the source is 200 V, find the maximum current.
(iii) Draw a graph showing variation of amplitude of circuit current with changing frequency of applied voltage in a series LRC circuit for two different values of resistance R1 and R2 (R1 > R2).
(iv) Define the term 'Sharpness of Resonance'. Under what condition, does a circuit become more selective?
When an AC source is connected to a capacitor, there is a steady-state current in the circuit. Does it mean that the charges jump from one plate to the other to complete the circuit?
Is energy produced when a transformer steps up the voltage?
A transformer is designed to convert an AC voltage of 220 V to an AC voltage of 12 V. If the input terminals are connected to a DC voltage of 220 V, the transformer usually burns. Explain.
The peak voltage of a 220 V AC source is
An AC source is rated 220 V, 50 Hz. The average voltage is calculated in a time interval of 0.01 s. It
The AC voltage across a resistance can be measured using
A bulb rated 60 W at 220 V is connected across a household supply of alternating voltage of 220 V. Calculate the maximum instantaneous current through the filament.
Compare resistance and reactance.
Suppose the initial charge on the capacitor is 6 mC. What is the total energy stored in the circuit initially? What is the total energy at later time?
Average power supplied to a capacitor over one complete cycle is ______.
If circuit containing capacitance only, the current ______.
A.C. power is transmitted from a power house at a high voltage as ______.
An alternating current of 1.5 mA and angular frequency 300 rad/sec flows through a 10 k Ω resistor and a 0.50 µF capacitor in series. Find the rms voltage across the capacitor and impedance of the circuit.
Define Capacitive reactance.
An a.c. source generating a voltage ε = ε0 sin ωt is connected to a capacitor of capacitance C. Find the expression for the current I flowing through it. Plot a graph of ε and I versus ωt to show that the current is ahead of the voltage by π/2.
An AC source is connected to a capacitor C. Due to decrease in its operating frequency ______.
A 40 µF capacitor is connected to a 200 V. 50 Hz ac supply. The rms value of the current on the circuit is, nearly ______.
In an ac circuit an alternating voltage e = 200\[\sqrt 2\] sin100t volts is connected to capacitor of capacity 1 µF. The r.m.s. value of the current in the circuit is ______.
In an alternating current circuit consisting of elements in series, the current increases on increasing the frequency of supply. Which of the following elements are likely to constitute the circuit?
When an AC voltage of 220 V is applied to the capacitor C ______.
A 10 µF capacitor is connected to a 210 V, 50 Hz source as shown in figure. The peak current in the circuit is nearly ______.
(π = 3.14)
