# Capacitor discharge: how is it measured?

• acherentia
In summary, the problem presented is in a calculus book and aims to illustrate the concept of a limit in experiments. The data describes the charge remaining on a camera's flash unit capacitor at various times after the flash goes off. To find the electric current flowing from the capacitor to the flashbulb, one can use the data to estimate the slope of the tangent line at t = 0.04 seconds. The easiest way to measure the discharge of a capacitor would be to measure the voltage across its terminals and calculate the charge using the formula Q = CV. This method assumes a constant capacitance and may not hold in extreme conditions.
acherentia
This is the problem and it's actually in my calculus book to illustrate the concept of a limit in experiments:

The flash unit on a camera operates by storing charge on a capacitor and releasing it suddenly when the flash is set off. The data in the table describe the charge Q remaining on the capacitor (measured in microcoulombs) at time t (measured in seconds after the flash goes off ).

{Use the data to draw the graph of this function and estimate the slope of the tangent line at the point where t = 0.04. [Note: The slope of the tangent line represents the electric current flowing from the capacitor to the flashbulb (measured in microamperes).]}

All I am wondering is how do they get the tabulated data of the charge on the capacitor at time t? How is that done experimentally?

Thank you

There are lots of ways to measure the discharge of a capacitor. The easiest way would probably be to measure a voltage which is proportional to the charge on a capacitor.

Does that make sense?

Hello acherentia,

acherentia said:
All I am wondering is how do they get the tabulated data of the charge on the capacitor at time t? How is that done experimentally?

Well, one can measure the voltage across capacitor's terminals (using a voltmeter, for example), and calculate the charge in the capacitor using

$$Q = CV.$$

This method approximates that the flash unit's capacitor's capacitance is truly constant (like an ideal capacitor), and is not a function of the voltage. Such an approximation should hold pretty well over the rated voltage range of a real-world capacitor. But it does have its limits in extreme conditions.

## 1. How is the capacitance of a capacitor measured?

The capacitance of a capacitor is typically measured using a capacitance meter, which sends a small known current through the capacitor and measures the resulting voltage. The capacitance is then calculated using the formula C = Q/V, where C is the capacitance, Q is the charge stored in the capacitor, and V is the voltage across the capacitor.

## 2. What is the difference between charging and discharging a capacitor?

Charging a capacitor involves applying a voltage across its terminals, causing it to store energy in the form of an electric field. Discharging a capacitor involves removing the voltage source, causing the stored energy to be released and the capacitor to return to its original state.

## 3. How is the voltage across a capacitor measured during discharge?

The voltage across a capacitor can be measured using a voltmeter connected across its terminals. As the capacitor discharges, the voltage will decrease and can be monitored on the voltmeter.

## 4. What factors affect the rate of discharge for a capacitor?

The rate of discharge for a capacitor is affected by the capacitance, the resistance of the circuit, and the voltage across the capacitor. A higher capacitance or lower resistance will result in a slower discharge, while a higher voltage will result in a faster discharge.

## 5. How do you calculate the time constant for a capacitor discharge?

The time constant, or the time it takes for a capacitor to discharge to 37% of its initial voltage, can be calculated using the formula τ = RC, where τ is the time constant, R is the resistance in the circuit, and C is the capacitance of the capacitor.

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