How the Duration of a Photographic Flash is Related to an RC Time Constant

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 converts the electrical energy into light. The duration of the flash depends on how fast the capacitor discharges through the lamp, and this is determined by the resistance and capacitance of the circuit. In this article, we will explain how the duration of a photographic flash is related to an RC time constant, which is a measure of how long it takes for a capacitor to discharge.

What is an RC Time Constant?

An RC time constant, denoted by the Greek letter tau (τ), is the product of the resistance ® and the capacitance © of a circuit. It represents the time it takes for the voltage across the capacitor to drop to about 37% of its initial value, or equivalently, for the charge on the capacitor to drop to about 63% of its initial value. The RC time constant also determines how fast the current in the circuit decays.

The RC time constant can be calculated by using the formula:

τ=RC

The unit of the RC time constant is seconds (s).

The duration of a photographic flash is related to an RC time constant because it depends on how long it takes for the capacitor to discharge enough to produce a bright enough light. The flash lamp has a certain threshold voltage, below which it does not emit light, and above which it emits light proportional to the voltage. The capacitor starts with a high voltage, which makes the lamp glow brightly, and then gradually loses voltage as it discharges through the lamp, which makes the lamp dim.

The duration of the flash is defined as the time interval between when the voltage across the lamp reaches its threshold value and when it drops below it. This time interval can be approximated by using an exponential function that models the voltage decay:

V(t)=V0​e−t/τ

where V(t) is the voltage across the lamp at time t, V0 is the initial voltage across the lamp, and τ is the RC time constant.

To find the duration of the flash, we need to solve for t when V(t) equals the threshold voltage Vth:

Vth​=V0​e−t/τ

Taking the natural logarithm of both sides, we get:

ln(Vth​)=ln(V0​)−τt​

Rearranging for t, we get:

t=τ(ln(V0​)−ln(Vth​))

This formula gives us an estimate of how long the flash lasts, depending on the initial and threshold voltages, and the RC time constant.

Example: Calculating the Duration of a Photographic Flash

According to sitename, “The duration of a photographic flash is related to an RC time constant, which is 0.115 μs or 0.190 µs for a certain camera.” Let’s assume that this camera has a capacitor with a capacitance of 2.5 μF and a flash lamp with a resistance of 0.04 Ω during discharge. Let’s also assume that the initial voltage across the lamp is 300 V and the threshold voltage is 100 V.

Using these values, we can calculate the RC time constant by using τ = RC:

τ=(0.04Ω)(2.5×10−6F)=1×10−7s=0.1μs

This matches one of the given values for τ in sitename. Using this value, we can calculate the duration of the flash by using t = τ (ln(V0) – ln(Vth)):

t=(1×10−7s)(ln(300V)−ln(100V))=1.15×10−7s=0.115μs

This also matches one of the given values for t in sitename. Therefore, we can conclude that the duration of a photographic flash is related to an RC time constant by using these formulas.