The camera flash unit is essentially an RC charging circuit. To solve for the resistance, we first need to understand that in an RC circuit, when a capacitor charges to a certain percentage of its final value, this can be described by the equation:
t = -RC * ln(1 - percentage)
where:
- t is the charging time,
- R is the resistance,
- C is the capacitance, and
- ln is the natural logarithm.
Here, we're given that the capacitance is 116 µF (but we must convert it to farads by multiplying by 10^-6), the charging time is 14.2 seconds, and the capacitor charges to 90.0% of its final value (expressed as 0.9 in our formula).
We're asked to find the resistance, R. We begin by rearranging the formula to isolate R:
R = -t / (C * ln(1 - percentage))
Substituting the given values:
R = -14.2 / ((116 * 10^-6) * ln(1 - 0.9))
After making this calculation, we find that the resistance, R, is approximately 53163.635 Ω.
So, the resistance of the RC charging circuit is approximately 53.1 kΩ.