Advertisements
Advertisements
Question
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
Solution
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
RELATED QUESTIONS
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.
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
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 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.
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.
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:
When a voltage measuring device is connected to AC mains, the meter shows the steady input voltage of 220V. This means ______.
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?
