Difference between revisions of "Dicharging a Capacitor"
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===About Capacitor Discharge=== | ===About Capacitor Discharge=== | ||
| − | *The [[Potential Difference|voltage]] and [[Electrical Current|current]] | + | *The [[Electrical Charge|charge]], [[Potential Difference|voltage]] and [[Electrical Current|current]] all decrease [[Exponential Decay|exponentially]] during '''discharge'''. |
| − | *The [[Time Constant|time constant]] determines how quickly a [[capacitor]] '''discharges'''. | + | *The [[Time Constant|time constant]] of a [[Electrical Circuit|circuit]] determines how quickly a [[capacitor]] '''discharges'''. |
| − | *A large [[time]] | + | *A large [[Time Constant|time constant]] means a slow '''discharge''', while a small [[Time Constant|time constant]] means a rapid '''discharge'''. |
*[[Capacitor]] '''discharge''' curves are used to analyze the behaviour of RC circuits. | *[[Capacitor]] '''discharge''' curves are used to analyze the behaviour of RC circuits. | ||
*Safety precautions are necessary when '''discharging''' large [[capacitor]]s to avoid [[Electrical Shock|electric shock]]. | *Safety precautions are necessary when '''discharging''' large [[capacitor]]s to avoid [[Electrical Shock|electric shock]]. | ||
===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>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]], | |
| − | 𝑄 | + | 𝐶 is the [[capacitance]] of the [[capacitor]], |
| + | |||
| + | 𝑡 is [[time]], | ||
| + | |||
| + | 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: | ||
| − | + | *𝜏 = 𝑅𝐶 | |
===Examples=== | ===Examples=== | ||
| − | In a [[defibrillator]], the capacitor discharges its energy quickly to deliver a shock to a patient's heart. | + | *In a [[defibrillator]], the [[capacitor]] '''discharges''' its energy quickly to deliver a shock to a patient's heart. |
| − | In RC timing circuits, | + | *In RC timing circuits, [[capacitor]]s '''discharge''' to control the timing intervals. |
Latest revision as of 18:14, 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 charge, voltage and current all decrease exponentially during discharge.
- The time constant of a circuit 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.