Electric Charge/Quantum/Examples/60W Bulb at 200V

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Example of Quanta of Electric Charge

Consider a $60 \ \mathrm W$ light bulb running at $200 \ \mathrm V$.

Approximately $2 \times 10^{18}$ units of elementary charge flow along the filament of the light bulb every second.


Proof

Let $n$ denote the number of units of elementary charge flow along the filament of the light bulb every second

The power $P$ dissipated in an electrical conductor is equal to the current $I$ flowing through it multiplied by the electric potential difference $V$ applied across it.

By definition, current $I$ equals the rate of flow of electric charge.


We have that a $60$ watt bulb with $200$ volts across it.

\(\ds I\) \(=\) \(\ds \dfrac V P\) Definition of Power
\(\ds \) \(=\) \(\ds \dfrac {60} {200} \ \mathrm A\) Definition of Watt
\(\ds \) \(=\) \(\ds \dfrac {60} {200} \ \mathrm C \ \mathrm s^{-1}\) Definition of Ampere
\(\ds \) \(=\) \(\ds \dfrac {60} {200} \times \dfrac 1 {1.60217 \, 6634 \times 10^{−19} } \ \mathrm e \ \mathrm s^{-1}\) Definition of Elementary Charge $\mathrm e$
\(\ds \leadsto \ \ \) \(\ds n\) \(=\) \(\ds \dfrac {60} {200} \times \dfrac 1 {1.60217 \, 6634 \times 10^{−19} }\) Definition of $n$
\(\ds \leadsto \ \ \) \(\ds n\) \(\approx\) \(\ds 1.87 \times 10^{18}\)

$\blacksquare$


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