Advertisements
Advertisements
Question
Explain why the reactance provided by a capacitor to an alternating current decreases with increasing frequency.
Advertisements
Solution
A capacitor does not allow flow of direct current through it as the resistance across the gap is infinite. When an alternating voltage is applied across the capacitor plates, the plates are alternately charged and discharged. The current through the capacitor is a result of this changing voltage (or charge). Thus, a capacitor will pass more current through it if the voltage is changing at a faster rate, i.e. if the frequency of supply is higher. This implies that the reactance offered by a capacitor is less with increasing frequency; it is given by 1/ωC.
APPEARS IN
RELATED QUESTIONS
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?
Show that the current leads the voltage in phase by π/2 in an AC circuit containing an ideal capacitor ?
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.
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
The dielectric strength of air is 3.0 × 106 V/m. A parallel-plate air-capacitor has area 20 cm2 and plate separation 0.10 mm. Find the maximum rms voltage of an AC source that can be safely connected to this capacitor.
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?
If circuit containing capacitance only, the current ______.
A capacitor has capacitance C and reactance X, if capacitance and frequency become double, then reactance will be ______.
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.
A device ‘X’ is connected to an a.c source. The variation of voltage, current and power in one complete cycle is shown in figure.
- Which curve shows power consumption over a full cycle?
- What is the average power consumption over a cycle?
- Identify the device ‘X’.
In the LCR circuit shown in figure, the ac driving voltage is v = vm sin ωt.
- Write down the equation of motion for q (t).
- At t = t0, the voltage source stops and R is short circuited. Now write down how much energy is stored in each of L and C.
- Describe subsequent motion of charges.
A resistor of 50 Ω, a capacitor of `(25/pi)` µF and an inductor of `(4/pi)` H are connected in series across an ac source whose voltage (in volts) is given by V = 70 sin (100 πt). Calculate:
- the net reactance of the circuit
- the impedance of the circuit
- the effective value of current in the circuit.
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 ______.
When an AC voltage of 220 V is applied to the capacitor C ______.
