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 $n$ | ||||||||||
\(\ds \leadsto \ \ \) | \(\ds n\) | \(\approx\) | \(\ds 1.87 \times 10^{18}\) |
$\blacksquare$
Sources
- 1958: C.A. Coulson: Electricity (5th ed.) ... (previous) ... (next): Chapter $\text {I}$: Preliminary Survey: $\S 1$. Electrostatics