Advertisements
Advertisements
प्रश्न
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.
Advertisements
उत्तर
Given:
Inductance of the coil, `L = 5.0 mH = 0.005 H`
(a) At ω = 100 s−1:
Reactance of coil `(X_L)` is given by,
`X_L = omegaL`
Here, `omega`= angular frequency
`therefore X_L = 100xx0.005 = 0.5 Ω`
peak current , `l_0 = 10/0.5 = 20 A`
(b) At `omega = 500 s^-1`
Reactance, `X_L = 500 xx 5/1000`
= 2.5 Ω
peak current, `l_0 = 10/2.5 = 4A`\
(c) ω = 1000 s−1:
`Reactance, X_L = 1000 xx 0.005 = 5 Ω`
Peak current, `l_0 = 10/5 = 2A`
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.
In a series LCR circuit connected to an ac source of variable frequency and voltage ν = vm sin ωt, draw a plot showing the variation of current (I) with angular frequency (ω) for two different values of resistance R1 and R2 (R1 > R2). Write the condition under which the phenomenon of resonance occurs. For which value of the resistance out of the two curves, a sharper resonance is produced? Define Q-factor of the circuit and give its significance.
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?
An alternating current is given by i = i1 cos ωt + i2 sin ωt. The rms current is given by
A constant current of 2.8 A exists in a resistor. The rms current is
An electric bulb is designed to operate at 12 volts DC. If this bulb is connected to an AC source and gives normal brightness, what would be the peak voltage of the source?
The peak power consumed by a resistive coil, when connected to an AC source, is 80 W. Find the energy consumed by the coil in 100 seconds, which is many times larger than the time period of the source.
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.
In a series RC circuit with an AC source, R = 300 Ω, C = 25 μF, ε0 = 50 V and ν = 50/π Hz. Find the peak current and the average power dissipated in the circuit.
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 peak voltage of an ac supply is 300 V. What is the rms voltage?
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’.]
A small town with a demand of 800 kW of electric power at 220 V is situated 15 km away from an electric plant generating power at 440 V. The resistance of the two wire line carrying power is 0.5 Ω per km. The town gets power from the line through a 4000-220 V step-down transformer at a sub-station in the town.
(a) Estimate the line power loss in the form of heat.
(b) How much power must the plant supply, assuming there is negligible power loss due to leakage?
(c) Characterise the step up transformer at the plant.
In a transformer Np = 500, Ns = 5000. Input voltage is 20 volt and frequency is 50 HZ. Then in the output, we have,
RMS value of an alternating current flowing in a circuit is 5A. Calculate its peak value.
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?
