Difference between revisions of "Dicharging a Capacitor"
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*<math>𝑄=𝑄_0𝑒^{−𝑡/𝑅𝐶}</math> | *<math>𝑄=𝑄_0𝑒^{−𝑡/𝑅𝐶}</math> | ||
| − | *<math>𝑄=𝑄_0𝑒^ | + | *<math>𝑄=𝑄_0𝑒^\frac{−𝑡}{𝑅𝐶}</math> |
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Revision as of 17:50, 22 May 2024
Key Stage 5
Meaning
Capacitor discharge is the process of releasing the stored energy in a capacitor through a circuit.
About Capacitor Discharge
- The voltage and current also decrease exponentially during discharge.
- The time constant determines how quickly a capacitor discharges.
- A large time constant means a slow discharge, while a small time constant means a rapid discharge.
- Capacitor discharge curves are used to analyze the behaviour of RC circuits.
- Safety precautions are necessary when discharging large capacitors to avoid electric shock.
Formula
The discharge through a resistor follows an exponential decay described by the formula:
- \(𝑄=𝑄_0𝑒^{−𝑡/𝑅𝐶}\)
- \(𝑄=𝑄_0𝑒^\frac{−𝑡}{𝑅𝐶}\)
Where:
𝑄 is the charge stored,
𝑄0 is the initial charge stored,
𝑅 is the resistance in the circuit,
𝐶 is the capacitance of the capacitor
and
𝑡 is time
A capacitor's rate of discharge in a circuit is characterised by the time constant 𝜏 which is given by the formula:
- 𝜏 = 𝑅𝐶
Examples
In a defibrillator, the capacitor discharges its energy quickly to deliver a shock to a patient's heart. In RC timing circuits, capacitors discharge to control the timing intervals.