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,
विकल्प
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?
Show that the current leads the voltage in phase by π/2 in an AC circuit containing an ideal capacitor ?
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?
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.
A capacitor acts as an infinite resistance for ______.
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 ‘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’.
Explain why the reactance provided by a capacitor to an alternating current decreases with increasing frequency.
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.
