Difference between revisions of "Dicharging a Capacitor"
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===Formula=== | ===Formula=== | ||
− | The '''discharge''' through a [[resistor]] follows an [[Exponential Decay|exponential decay]] described by the | + | The '''discharge''' through a [[resistor]] follows an [[Exponential Decay|exponential decay]] described by the formulae: |
*<math>𝑄=𝑄_0𝑒^{−𝑡/𝑅𝐶}</math> | *<math>𝑄=𝑄_0𝑒^{−𝑡/𝑅𝐶}</math> | ||
− | *<math> | + | |
+ | *<math>V=V_0𝑒^{−𝑡/𝑅𝐶}</math> | ||
+ | |||
+ | *<math>I=I_0𝑒^{−𝑡/𝑅𝐶}</math> | ||
+ | |||
Where: | Where: | ||
− | + | 𝑅 is the [[Electrical Resistance|resistance]] in the [[Electrical Circuit|circuit]], | |
+ | |||
+ | 𝐶 is the [[capacitance]] of the [[capacitor]], | ||
+ | |||
+ | 𝑡 is [[time]], | ||
− | 𝑄 | + | 𝑄 is the [[Electrical Charge|charge]] stored at time t, |
+ | |||
+ | V is the [[Potential Difference|potential difference]] across the [[capacitor]] at time t, | ||
− | + | I is the [[Electrical Current|current]] being discharged by the [[capacitor]] at time t, | |
− | + | 𝑄<sub>0</sub> is the initial [[Electrical Charge|charge]] stored, | |
− | + | V<sub>0</sub> is the initial [[Potential Difference|potential difference]] across the [[capacitor]], | |
− | + | I<sub>0</sub> is the initial [[Electrical Current|current]] through the [[Electrical Circuit|circuit]] | |
A [[capacitor]]'s rate of '''discharge''' in a [[Electrical Circuit|circuit]] is characterised by the [[Capacitor Time Constant|time constant]] 𝜏 which is given by the formula: | A [[capacitor]]'s rate of '''discharge''' in a [[Electrical Circuit|circuit]] is characterised by the [[Capacitor Time Constant|time constant]] 𝜏 which is given by the formula: |
Revision as of 17:55, 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 formulae:
- \(𝑄=𝑄_0𝑒^{−𝑡/𝑅𝐶}\)
- \(V=V_0𝑒^{−𝑡/𝑅𝐶}\)
- \(I=I_0𝑒^{−𝑡/𝑅𝐶}\)
Where:
𝑅 is the resistance in the circuit,
𝐶 is the capacitance of the capacitor,
𝑡 is time,
𝑄 is the charge stored at time t,
V is the potential difference across the capacitor at time t,
I is the current being discharged by the capacitor at time t,
𝑄0 is the initial charge stored,
V0 is the initial potential difference across the capacitor,
I0 is the initial current through the circuit
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.