Advertisements
Advertisements
प्रश्न
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?
Advertisements
उत्तर
Voltage across the electric bulb, E = 12 volts
Let E0 be the peak value of voltage.
We know that heat produced by passing an alternating current ( i ) through a resistor is equal to heat produced by passing a constant current `(i_{rms})`through the same resistor. If R is the resistance of the electric bulb and T is the temperature, then
`i^2RT = i^2_rms^{RT}`
`⇒ E^2/R^2 = E_{rms}^2/R^2`
`⇒ E^2 = E_0^2/2 (therefore E^2_rms = E_0^2)`
`⇒ E_0^2 = 2E^2`
`⇒ E_0^2 = 2xx(12)^2`
⇒ E02 = 2 × 144
`⇒ E_0 = sqrt(2 xx 144)`
`⇒ E_0 = sqrt(2) xx 12`
`⇒ E_0 = 1.4142 xx 12`
⇒ E0 = 16.9704
= 16.97 ≈ 17 V
Thus , peak value of voltage is 17 V.
APPEARS IN
संबंधित प्रश्न
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.
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 is given by i = i1 cos ωt + i2 sin ωt. The rms current is given by
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
A constant current of 2.8 A exists in a resistor. The rms current 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.
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.
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 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.
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?
If `|vec"A" xx vec"B"| = sqrt3 vec"A" . vec"B"` then the value of is `|vec"A" xx vec"B"|` is
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:
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?
