Advertisements
Advertisements
प्रश्न
The voltage and current in a series AC circuit are given by V = V0cos ωt and i = i0 sin ωt. What is the power dissipated in the circuit?
Advertisements
उत्तर
Voltage, V = V0cos ωt
Current, i = i0 sin ωt or i = i0 cos (`wt - pi/2`)
Power dissipated in an AC circuit is given by,
`P = I_rms V_rms cos Ø`,
where Irms = rms value of current
Vrms= rms value of voltage
ϕ = phase difference between current and voltage
Here, ϕ = `pi`/2
⇒ `cos Ø = cos pi/2 = 0`
∴` P = Irms Vrms xx o = 0`
APPEARS IN
संबंधित प्रश्न
A device X is connected across an ac source of voltage V = V0 sin ωt. The current through X is given as
`I = I_0 sin (omega t + pi/2 )`
1) Identify the device X and write the expression for its reactance.
2) Draw graphs showing the variation of voltage and current with time over one cycle of ac, for X.
3) How does the reactance of the device X vary with the frequency of the ac? Show this variation graphically.
4) Draw the phasor diagram for the device X.
Two alternating currents are given by `i_1 = i_0 sin wt and i_2 = i_0 sin (wt + pi/3)` Will the rms values of the currents be equal or different?
Can the peak voltage across the inductor be greater than the peak voltage of the source in an LCR circuit?
An alternating current of peak value 14 A is used to heat a metal wire. To produce the same heating effect, a constant current i can be used, where i is
The household supply of electricity is at 220 V (rms value) and 50 Hz. Find the peak voltage and the least possible time in which the voltage can change from the rms value to zero.
A capacitor of capacitance 10 μF is connected to an oscillator with output voltage ε = (10 V) sin ωt. Find the peak currents in the circuit for ω = 10 s−1, 100 s−1, 500 s−1 and 1000 s−1.
A coil of inductance 5.0 mH and negligible resistance is connected to the oscillator of the previous problem. Find the peak currents in the circuit for ω = 100 s−1, 500 s−1, 1000 s−1.
A resistor of resistance 100 Ω is connected to an AC source ε = (12 V) sin (250 π s−1)t. Find the energy dissipated as heat during t = 0 to t = 1.0 ms.
Answer the following question.
A small town with a demand of 1200 kW of electric power at 220 V is situated 20 km away from an electric plant generating power at 440 V. The resistance of the two wirelines carrying power is 0.5 Ω per km. The town gets the power from the line through a 4000-220 V step-down transformer at a sub-station in the town. Estimate the line power loss in the form of heat.
The rms value of current in an ac circuit is 10 A. What is the peak current?
A circuit containing a 80 mH inductor and a 60 µF capacitor in series is connected to a 230 V, 50 Hz supply. The resistance of the circuit is negligible.
(a) Obtain the current amplitude and rms values.
(b) Obtain the rms values of potential drops across each element.
(c) What is the average power transferred to the inductor?
(d) What is the average power transferred to the capacitor?
(e) What is the total average power absorbed by the circuit?
[‘Average’ implies ‘averaged over one cycle’.]
Do the same with the replacement of the earlier transformer by a 40,000-220 V step-down transformer (Neglect, as before, leakage losses though this may not be a good assumption any longer because of the very high voltage transmission involved). Hence, explain why high voltage transmission is preferred?
The period of oscillation of a simple pendulum is T = `2π sqrt"L"/"g"`. The measured value of L is 20.0 cm known to have 1 mm accuracy and the time for 100 oscillations of the pendulum is found to be 90 s using a wristwatch of ls resolution. The accuracy in the determination of g is:
Phase diffn between voltage and current in a capacitor in A.C Circuit is.
In a transformer Np = 500, Ns = 5000. Input voltage is 20 volt and frequency is 50 HZ. Then in the output, we have,
In the Figure below, the current-voltage graphs for a conductor are given at two different temperatures, T1 and T2.
- At which temperature T1 or T2 is the resistance higher?
- Which temperature (T1 or T2) is higher?
