A photographic flash is a device that produces a brief and intense burst of light to illuminate a scene for photography. The flash is usually powered by a capacitor, which stores electrical energy and releases it quickly when triggered. The capacitor is connected to a flash lamp, which is a type of electric light that emits light when an electric current passes through it. The flash lamp has a certain resistance, which limits the amount of current that flows through it.
The duration of the flash depends on how long it takes for the capacitor to discharge through the flash lamp. This process can be modeled by an RC circuit, which is a simple electrical circuit that consists of a resistor and a capacitor. An RC circuit has a characteristic time constant, which is the product of the resistance and the capacitance. The time constant determines how fast the capacitor charges or discharges.
The Flash Discharge Time
According to bartleby.com, the duration of a photographic flash is related to an RC time constant, which is 0.115 μs during the flash discharge for a certain camera. This means that the capacitor loses about 63% of its initial voltage in 0.115 μs when connected to the flash lamp.
If we know the resistance of the flash lamp, we can calculate the capacitance of the capacitor using the formula:
$$C = \frac{\tau}{R}$$
where C is the capacitance, τ is the time constant, and R is the resistance.
For example, if the resistance of the flash lamp is 0.048 Ω during discharge, as given by another answer on bartleby.com⁴, then the capacitance of the capacitor is:
$$C = \frac{0.115 \times 10^{-6}}{0.048}$$
$$C = 2.40 \times 10^{-6} F$$
or 2.40 μF.
The Flash Charging Time
The capacitor needs to be charged before it can be used for another flash. The charging time depends on the source of power, which usually has a higher resistance than the flash lamp. The charging time can also be modeled by an RC circuit, but with a different time constant.
The time constant for charging the capacitor is given by:
$$\tau’ = R’C$$
where τ’ is the charging time constant, R’ is the charging resistance, and C is the capacitance.
For example, if the charging resistance is 800 kΩ, as given by collegephysicsanswers.com², then the charging time constant for a 2.40 μF capacitor is:
$$\tau’ = 800 \times 10^3 \times 2.40 \times 10^{-6}$$
$$\tau’ = 1.92 s$$
This means that it takes about 1.92 s for the capacitor to reach about 63% of its maximum voltage when connected to the power source.
The actual charging time may vary depending on the initial and final voltages of the capacitor and the power source. A common rule of thumb is that it takes about five time constants for the capacitor to charge to more than 99% of its maximum voltage.
Conclusion
The duration of a photographic flash is related to an RC time constant, which depends on the resistance and capacitance of the circuit. The flash discharge time is shorter than the flash charging time, because the flash lamp has a lower resistance than the power source. The capacitance of the capacitor determines how much energy can be stored and released for each flash.
