Advertisements
Advertisements
प्रश्न
An AC source producing emf ε = ε0 [cos (100 π s−1)t + cos (500 π s−1)t] is connected in series with a capacitor and a resistor. The steady-state current in the circuit is found to be i = i1 cos [(100 π s−1)t + φ1) + i2 cos [(500π s−1)t + ϕ2]. So,
पर्याय
i1 > i2
i1 = i2
i1 < i2
The information is insufficient to find the relation between i1 and i2.
Advertisements
उत्तर
i1 < i2
The charge on the capacitor during steady state is given by,
`Q = C epsilon = epsilon _0C [cos(100pis^-1)]`
the steady state current is, thus, given by,
`i =(dQ)/dt = epsilon _0Cxx100pi [sin(100pis^-1)] + epsilon_0Cxx 500pi [sin({00pis)]`
c`
⇒ i = 100Cepsilon cos [(100pis^-1)] t + Ø_1+500piepsilon_0 cos [(500pis^-1)] + Ø_2]`
⇒ `i_1 = 100Cpiepsilon_0 & i_2 = 500C_piepsilon_0`
∴ i_2 > i_1
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?
A current i1 = i0 sin ωt passes through a resistor of resistance R. How much thermal energy is produced in one time period? A current i2 = −i0 sin ωt passes through the resistor. How much thermal energy is produced in one time period? If i1 and i2 both pass through the resistor simultaneously, how much thermal energy is produced? Is the principle of superposition obeyed in this case?
Is energy produced when a transformer steps up the voltage?
A capacitor acts as an infinite resistance for ______.
An AC source is rated 220 V, 50 Hz. The average voltage is calculated in a time interval of 0.01 s. It
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.
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?
Compare resistance and reactance.
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.
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 ______.
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.
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.
