A Christmas light is made to flash via the dischar...

Question

A Christmas light is made to flash via the discharge of a capacitor. The effective duration of the flash is 0.23 s (which you can assume is the time constant of the capacitor), during which it produces an average 75 mW from an average voltage of 3.15 V.

Part (a). How much energy, in joules, does it dissipate?

Part (b). How much charge, coulombs, moves through the light?

Part (c). Find the capacitance of the light, in farads.

Part (d). What is the resistance, in ohms, of the light?

Patrick Ford · Accepted Answer

We have the following information:Duration of the flash, t = 0.23sPower, P = 75 mWVoltage, V = 3.15V[readmore]Part (a)Electric power:P=EtThis means that E = PtE = (75 × 10-3)(0.23) = 0.01725 JThe amount of energy that the Christmas light dissipates is 0.01725 J.Part (b)Electric current:i=qtThus, the charge, q is given by:q=itBut we know that:P = iV, which gives:i = P/VTherefore, q=PtV=(75×10-3)(0.23)3.15q = 5.476 × 10-3 CThe amount of charge that moves through the light is 5.476 × 10-3 C.Part (c)Capacitance is given by:C=qV=5.476×10-33.15C = 1.738 × 10-3 FThe capacitance of the light is 1.738 × 10-3 F. Part (d)The time constant of an RC circuit is expressed as:τ=RCThe capacitor is discharged through a resistor at a time, t.This implies that t = 𝜏Therefore,R = 𝜏/C = 0.23/(1.738 × 10-3) = 132.34 ΩResistance of the light is 132.34 Ω.

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