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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 - Physics


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?

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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 = 2 xx 144`

`⇒ E_0= sqrt2xx144`

 =16.97 = 17 ⇒ V

Thus , peak value of voltage is 17 V.

Concept: Peak and Rms Value of Alternating Current Or Voltage
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HC Verma Class 11, Class 12 Concepts of Physics Vol. 2
Chapter 17 Alternating Current
Q 4 | Page 330
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