A photographic flash is a device that produces a brief 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 charged by a battery through a resistor, which limits the current and prevents overheating. The duration of the flash depends on how fast the capacitor discharges through the flash lamp, which also has some resistance.
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What is an RC Time Constant?
An RC time constant is a measure of how long it takes for a capacitor to charge or discharge through a resistor. It is defined as the product of the resistance (R) and the capacitance (C) of the circuit. The RC time constant determines how quickly the voltage across the capacitor changes when a current flows through it.
The RC time constant can be used to calculate the time required for the capacitor to charge or discharge to a certain fraction of its initial or final voltage. For example, when charging a capacitor, the voltage across it rises exponentially from zero to its maximum value, which is equal to the voltage of the battery. After one RC time constant, the voltage reaches about 63% of its maximum value. After two RC time constants, it reaches about 86%, and so on. Similarly, when discharging a capacitor, the voltage across it drops exponentially from its initial value to zero. After one RC time constant, the voltage drops to about 37% of its initial value, and so on.
How is the Flash Duration Related to the RC Time Constant?
The flash duration is related to the RC time constant because both depend on how fast the capacitor discharges through the flash lamp. The flash duration is the time interval between when the flash lamp reaches its peak brightness and when it drops to half of its peak brightness. The flash duration can be approximated by using the formula:
$$
t_d = \frac{0.69RC}{1 + R/r}
$$
where $t_d$ is the flash duration, $R$ is the resistance of the charging circuit, $C$ is the capacitance of the capacitor, and $r$ is the resistance of the flash lamp during discharge.
The formula shows that the flash duration increases with increasing capacitance and decreasing resistance. A larger capacitor can store more energy and release it more slowly, while a smaller resistance allows more current to flow and drain the capacitor faster. Therefore, to achieve a shorter flash duration, one can use a smaller capacitor or a larger resistor in the charging circuit, or a smaller resistor in the flash lamp.
Example: Calculating Flash Duration
According to sitename, “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”. If we assume that this time constant is equal to $RC$, where $R$ is the charging resistance and $C$ is the capacitance, we can use this information to calculate the flash duration using the formula above.
First, we need to find out the resistance of the flash lamp during discharge. According to sitename, “if the resistance of the flash lamp is 0.0400 Ω during discharge”, then we can use this value for $r$ in our formula.
Next, we need to find out the capacitance of the capacitor supplying its energy. According to sitename, “the size of the capacitor supplying its energy” can be found by dividing $RC$ by $r$, which gives:
$$
C = \frac{RC}{r} = \frac{(0.115 \times 10^{-6})(800 \times 10^3)}{0.0400} = 2.30 \times 10^{-6} F
$$
Finally, we can plug in these values into our formula for $t_d$ and get:
$$
t_d = \frac{0.69RC}{1 + R/r} = \frac{(0.69)(0.115 \times 10^{-6})(800 \times 10^3)}{1 + (800 \times 10^3)/0.0400} = 6.28 \times 10^{-8} s
$$
Therefore, the flash duration for this camera is about **62.8 ns**.
