Advertisements
Advertisements
प्रश्न
Show that the current leads the voltage in phase by π/2 in an AC circuit containing an ideal capacitor ?
Advertisements
उत्तर
Let us consider a capacitor C connected to an AC source as shown below.
Let the AC voltage applied be
`v = v_msinωt`
`∴ v = q/C`
Applying Kirchhoff’s loop rule, we have:
` v_msinωt q/C`
`i = (dq)/dt`
`∴ i = (d)/dt( v_mCsinωt) `
`ωCv_mcos(ωt)`
`cos ωt = sinωt+π/2`
`∴ i = i_msin(ωt+π/2)`
`i_m = ωCv_m`
`i =(v_m)/((1/(ωC)))`
संबंधित प्रश्न
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.
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.
A transformer has 50 turns in the primary and 100 in the secondary. If the primary is connected to a 220 V DC supply, what will be the voltage across the secondary?
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.
Average power supplied to a capacitor over one complete cycle is ______.
An iron cored coil is connected in series with an electric bulb with an AC source as shown in figure. When iron piece is taken out of the coil, the brightness of the bulb will ______.
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.
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?
